Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$
Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
McGonagle, Matthew [verfasserIn] Xiao, Ling [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: The journal of geometric analysis - New York, NY : Springer, 1991, 30(2019), 2 vom: 20. März, Seite 2189-2224 |
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| Übergeordnetes Werk: |
volume:30 ; year:2019 ; number:2 ; day:20 ; month:03 ; pages:2189-2224 |
| Links: |
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| DOI / URN: |
10.1007/s12220-019-00179-2 |
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| Katalog-ID: |
SPR039274845 |
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| 520 | |a Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. | ||
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| 700 | 1 | |a Xiao, Ling |e verfasserin |4 aut | |
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10.1007/s12220-019-00179-2 doi (DE-627)SPR039274845 (SPR)s12220-019-00179-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.52 bkl McGonagle, Matthew verfasserin aut Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. Minimal graph (dpeaa)DE-He213 Graphical mean curvature flow (dpeaa)DE-He213 Manifolds (dpeaa)DE-He213 Xiao, Ling verfasserin aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 30(2019), 2 vom: 20. März, Seite 2189-2224 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:30 year:2019 number:2 day:20 month:03 pages:2189-2224 https://dx.doi.org/10.1007/s12220-019-00179-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 31.52 ASE AR 30 2019 2 20 03 2189-2224 |
| spelling |
10.1007/s12220-019-00179-2 doi (DE-627)SPR039274845 (SPR)s12220-019-00179-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.52 bkl McGonagle, Matthew verfasserin aut Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. Minimal graph (dpeaa)DE-He213 Graphical mean curvature flow (dpeaa)DE-He213 Manifolds (dpeaa)DE-He213 Xiao, Ling verfasserin aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 30(2019), 2 vom: 20. März, Seite 2189-2224 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:30 year:2019 number:2 day:20 month:03 pages:2189-2224 https://dx.doi.org/10.1007/s12220-019-00179-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 31.52 ASE AR 30 2019 2 20 03 2189-2224 |
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10.1007/s12220-019-00179-2 doi (DE-627)SPR039274845 (SPR)s12220-019-00179-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.52 bkl McGonagle, Matthew verfasserin aut Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. Minimal graph (dpeaa)DE-He213 Graphical mean curvature flow (dpeaa)DE-He213 Manifolds (dpeaa)DE-He213 Xiao, Ling verfasserin aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 30(2019), 2 vom: 20. März, Seite 2189-2224 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:30 year:2019 number:2 day:20 month:03 pages:2189-2224 https://dx.doi.org/10.1007/s12220-019-00179-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 31.52 ASE AR 30 2019 2 20 03 2189-2224 |
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10.1007/s12220-019-00179-2 doi (DE-627)SPR039274845 (SPR)s12220-019-00179-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.52 bkl McGonagle, Matthew verfasserin aut Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. Minimal graph (dpeaa)DE-He213 Graphical mean curvature flow (dpeaa)DE-He213 Manifolds (dpeaa)DE-He213 Xiao, Ling verfasserin aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 30(2019), 2 vom: 20. März, Seite 2189-2224 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:30 year:2019 number:2 day:20 month:03 pages:2189-2224 https://dx.doi.org/10.1007/s12220-019-00179-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 31.52 ASE AR 30 2019 2 20 03 2189-2224 |
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10.1007/s12220-019-00179-2 doi (DE-627)SPR039274845 (SPR)s12220-019-00179-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.52 bkl McGonagle, Matthew verfasserin aut Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. Minimal graph (dpeaa)DE-He213 Graphical mean curvature flow (dpeaa)DE-He213 Manifolds (dpeaa)DE-He213 Xiao, Ling verfasserin aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 30(2019), 2 vom: 20. März, Seite 2189-2224 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:30 year:2019 number:2 day:20 month:03 pages:2189-2224 https://dx.doi.org/10.1007/s12220-019-00179-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 31.52 ASE AR 30 2019 2 20 03 2189-2224 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR039274845</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220111125423.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2019 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12220-019-00179-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR039274845</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12220-019-00179-2-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.52</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">McGonagle, Matthew</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). 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minimal graphs and graphical mean curvature flow in %$m^n\times \mathbb {r}%$ |
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Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$ |
| abstract |
Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. |
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Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. |
| abstract_unstemmed |
Abstract In this paper, we investigate the problem of finding minimal graphs in %$M^n\times \mathbb {R}%$ with general boundary conditions using a variational approach. Following Giusti (Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Birkhäuser Verlag, Basel, 1984), we study the so-called generalized solutions that minimize the adapted area functional (AAF) (1.2). We also show that when the boundary data %$\varphi %$ satisfy certain conditions, the generalized solution is actually the classical solution. This generalizes the results in Schulz–Williams (Analysis 7(3–4):359–374, 1987) to %$M^n\times \mathbb {R}.%$ Finally, following the idea of Oliker–Ural’tseva (Commun Pure Appl Math 46(1):97–135, 1993 and Topol Methods Nonlinear Anal 9(1):17–28, 1997), we consider the long time existence and convergence of the graphical mean curvature flow (1.3). We show that as %$t\rightarrow \infty ,%%%$u(\cdot , t)\rightarrow \bar{u},%$ where %$\bar{u}%$ is a generalized solution to the associated Dirichlet problem. |
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Minimal Graphs and Graphical Mean Curvature Flow in %$M^n\times \mathbb {R}%$ |
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https://dx.doi.org/10.1007/s12220-019-00179-2 |
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Xiao, Ling |
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2024-07-03T23:02:55.915Z |
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| score |
7.398512 |