CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$

Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with...
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Gespeichert in:

Autor*in:	Aiolfi, Ari J. [verfasserIn] Klaser, Patrícia

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	CMC graphs Planar boundary Unbounded domains

Anmerkung:	© Sociedade Brasileira de Matemática 2022

Übergeordnetes Werk:	Enthalten in: Bulletin of the Brazilian Mathematical Society - Heidelberg [u.a.] : Springer, 1970, 53(2022), 3 vom: 22. März, Seite 909-924
Übergeordnetes Werk:	volume:53 ; year:2022 ; number:3 ; day:22 ; month:03 ; pages:909-924

Links:	Volltext

DOI / URN:	10.1007/s00574-022-00288-7

Katalog-ID:	SPR047727675

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520			\|a Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$
650		4	\|a CMC graphs \|7 (dpeaa)DE-He213
650		4	\|a Planar boundary \|7 (dpeaa)DE-He213
650		4	\|a Unbounded domains \|7 (dpeaa)DE-He213
700	1		\|a Klaser, Patrícia \|0 (orcid)0000-0002-0671-881X \|4 aut
773	0	8	\|i Enthalten in \|t Bulletin of the Brazilian Mathematical Society \|d Heidelberg [u.a.] : Springer, 1970 \|g 53(2022), 3 vom: 22. März, Seite 909-924 \|w (DE-627)356885062 \|w (DE-600)2093151-7 \|x 1678-7714 \|7 nnns
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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allfields	10.1007/s00574-022-00288-7 doi (DE-627)SPR047727675 (SPR)s00574-022-00288-7-e DE-627 ger DE-627 rakwb eng Aiolfi, Ari J. verfasserin (orcid)0000-0002-8330-598X aut CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ CMC graphs (dpeaa)DE-He213 Planar boundary (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Klaser, Patrícia (orcid)0000-0002-0671-881X aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 3 vom: 22. März, Seite 909-924 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:3 day:22 month:03 pages:909-924 https://dx.doi.org/10.1007/s00574-022-00288-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 3 22 03 909-924
spelling	10.1007/s00574-022-00288-7 doi (DE-627)SPR047727675 (SPR)s00574-022-00288-7-e DE-627 ger DE-627 rakwb eng Aiolfi, Ari J. verfasserin (orcid)0000-0002-8330-598X aut CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ CMC graphs (dpeaa)DE-He213 Planar boundary (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Klaser, Patrícia (orcid)0000-0002-0671-881X aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 3 vom: 22. März, Seite 909-924 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:3 day:22 month:03 pages:909-924 https://dx.doi.org/10.1007/s00574-022-00288-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 3 22 03 909-924
allfields_unstemmed	10.1007/s00574-022-00288-7 doi (DE-627)SPR047727675 (SPR)s00574-022-00288-7-e DE-627 ger DE-627 rakwb eng Aiolfi, Ari J. verfasserin (orcid)0000-0002-8330-598X aut CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ CMC graphs (dpeaa)DE-He213 Planar boundary (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Klaser, Patrícia (orcid)0000-0002-0671-881X aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 3 vom: 22. März, Seite 909-924 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:3 day:22 month:03 pages:909-924 https://dx.doi.org/10.1007/s00574-022-00288-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 3 22 03 909-924
allfieldsGer	10.1007/s00574-022-00288-7 doi (DE-627)SPR047727675 (SPR)s00574-022-00288-7-e DE-627 ger DE-627 rakwb eng Aiolfi, Ari J. verfasserin (orcid)0000-0002-8330-598X aut CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ CMC graphs (dpeaa)DE-He213 Planar boundary (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Klaser, Patrícia (orcid)0000-0002-0671-881X aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 3 vom: 22. März, Seite 909-924 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:3 day:22 month:03 pages:909-924 https://dx.doi.org/10.1007/s00574-022-00288-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 3 22 03 909-924
allfieldsSound	10.1007/s00574-022-00288-7 doi (DE-627)SPR047727675 (SPR)s00574-022-00288-7-e DE-627 ger DE-627 rakwb eng Aiolfi, Ari J. verfasserin (orcid)0000-0002-8330-598X aut CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ CMC graphs (dpeaa)DE-He213 Planar boundary (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Klaser, Patrícia (orcid)0000-0002-0671-881X aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 3 vom: 22. März, Seite 909-924 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:3 day:22 month:03 pages:909-924 https://dx.doi.org/10.1007/s00574-022-00288-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 3 22 03 909-924
language	English
source	Enthalten in Bulletin of the Brazilian Mathematical Society 53(2022), 3 vom: 22. März, Seite 909-924 volume:53 year:2022 number:3 day:22 month:03 pages:909-924
sourceStr	Enthalten in Bulletin of the Brazilian Mathematical Society 53(2022), 3 vom: 22. März, Seite 909-924 volume:53 year:2022 number:3 day:22 month:03 pages:909-924
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	CMC graphs Planar boundary Unbounded domains
isfreeaccess_bool	false
container_title	Bulletin of the Brazilian Mathematical Society
authorswithroles_txt_mv	Aiolfi, Ari J. @@aut@@ Klaser, Patrícia @@aut@@
publishDateDaySort_date	2022-03-22T00:00:00Z
hierarchy_top_id	356885062
id	SPR047727675
language_de	englisch
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author	Aiolfi, Ari J.
spellingShingle	Aiolfi, Ari J. misc CMC graphs misc Planar boundary misc Unbounded domains CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$
authorStr	Aiolfi, Ari J.
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topic_title	CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$ CMC graphs (dpeaa)DE-He213 Planar boundary (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213
topic	misc CMC graphs misc Planar boundary misc Unbounded domains
topic_unstemmed	misc CMC graphs misc Planar boundary misc Unbounded domains
topic_browse	misc CMC graphs misc Planar boundary misc Unbounded domains
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$
ctrlnum	(DE-627)SPR047727675 (SPR)s00574-022-00288-7-e
title_full	CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$
author_sort	Aiolfi, Ari J.
journal	Bulletin of the Brazilian Mathematical Society
journalStr	Bulletin of the Brazilian Mathematical Society
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author_browse	Aiolfi, Ari J. Klaser, Patrícia
container_volume	53
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author-letter	Aiolfi, Ari J.
doi_str_mv	10.1007/s00574-022-00288-7
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title_sort	cmc graphs with planar boundary in %$\mathbb {h}^{2}\times \mathbb {r}%$
title_auth	CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$
abstract	Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ © Sociedade Brasileira de Matemática 2022
abstractGer	Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ © Sociedade Brasileira de Matemática 2022
abstract_unstemmed	Abstract Let %$\Omega \subset \mathbb {R}^{2}%$ be an unbounded convex domain. It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. We also present more refined existence results involving the curvature of %$\partial \Omega %$, which can also be less than %$-1.%$ © Sociedade Brasileira de Matemática 2022
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title_short	CMC Graphs with Planar Boundary in %$\mathbb {H}^{2}\times \mathbb {R}%$
url	https://dx.doi.org/10.1007/s00574-022-00288-7
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author2	Klaser, Patrícia
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doi_str	10.1007/s00574-022-00288-7
up_date	2024-07-03T14:35:38.528Z
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It is proven in López (J Diff Equ 171:54–62, 2001) and Ripoll (Pac J Math 198(1):175–196, 2001) that, given %$H>0%$, there exists a graph %$G\subset \mathbb {R}^{3}%$ of constant mean curvature H over %$\Omega %$ with %$\partial G=\partial \Omega %$ if and only if %$\Omega %$ is included in a strip of width 1/H. In this paper we obtain results in %$\mathbb {H}^{2}\times \mathbb {R}%$ in the same direction: given %$H\in \left( 0,1/2\right) %$, if %$\Omega %$ is included in a region of %$\mathbb {H}^{2}\times \left\{ 0\right\} %$ bounded by two hypercircles equidistant %$\ell (H)%$ to a same geodesic, we show that, if the geodesic curvature of %$\partial \Omega %$ is bounded from below by %$-1,%$ then there is an H-graph G over %$\Omega %$ with %$\partial G=\partial \Omega %$. 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März, Seite 909-924</subfield><subfield code="w">(DE-627)356885062</subfield><subfield code="w">(DE-600)2093151-7</subfield><subfield code="x">1678-7714</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:53</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:3</subfield><subfield code="g">day:22</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:909-924</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00574-022-00288-7</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" 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