On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type
Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Jimenez-Lopez, Francisco G. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
Asymptotic length spectrum Teichmüller space |
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| Anmerkung: |
© Sociedad Matemática Mexicana 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Boletin de la Sociedad Matemática Mexicana - New York [u.a.] : Springer International, 2014, 25(2017), 1 vom: 16. Nov., Seite 131-144 |
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| Übergeordnetes Werk: |
volume:25 ; year:2017 ; number:1 ; day:16 ; month:11 ; pages:131-144 |
| Links: |
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| DOI / URN: |
10.1007/s40590-017-0188-0 |
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| Katalog-ID: |
SPR036692050 |
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| 100 | 1 | |a Jimenez-Lopez, Francisco G. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type |
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| 520 | |a Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. | ||
| 650 | 4 | |a Asymptotic length spectrum Teichmüller space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Length spectrum Teichmüller space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Length spectrum metric |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Surfaces of infinite type |7 (dpeaa)DE-He213 | |
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| 773 | 1 | 8 | |g volume:25 |g year:2017 |g number:1 |g day:16 |g month:11 |g pages:131-144 |
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10.1007/s40590-017-0188-0 doi (DE-627)SPR036692050 (SPR)s40590-017-0188-0-e DE-627 ger DE-627 rakwb eng Jimenez-Lopez, Francisco G. verfasserin aut On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Matemática Mexicana 2017 Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. Asymptotic length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum metric (dpeaa)DE-He213 Surfaces of infinite type (dpeaa)DE-He213 Enthalten in Boletin de la Sociedad Matemática Mexicana New York [u.a.] : Springer International, 2014 25(2017), 1 vom: 16. Nov., Seite 131-144 (DE-627)779395166 (DE-600)2757902-5 2296-4495 nnns volume:25 year:2017 number:1 day:16 month:11 pages:131-144 https://dx.doi.org/10.1007/s40590-017-0188-0 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 16 11 131-144 |
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10.1007/s40590-017-0188-0 doi (DE-627)SPR036692050 (SPR)s40590-017-0188-0-e DE-627 ger DE-627 rakwb eng Jimenez-Lopez, Francisco G. verfasserin aut On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Matemática Mexicana 2017 Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. Asymptotic length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum metric (dpeaa)DE-He213 Surfaces of infinite type (dpeaa)DE-He213 Enthalten in Boletin de la Sociedad Matemática Mexicana New York [u.a.] : Springer International, 2014 25(2017), 1 vom: 16. Nov., Seite 131-144 (DE-627)779395166 (DE-600)2757902-5 2296-4495 nnns volume:25 year:2017 number:1 day:16 month:11 pages:131-144 https://dx.doi.org/10.1007/s40590-017-0188-0 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 16 11 131-144 |
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10.1007/s40590-017-0188-0 doi (DE-627)SPR036692050 (SPR)s40590-017-0188-0-e DE-627 ger DE-627 rakwb eng Jimenez-Lopez, Francisco G. verfasserin aut On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Matemática Mexicana 2017 Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. Asymptotic length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum metric (dpeaa)DE-He213 Surfaces of infinite type (dpeaa)DE-He213 Enthalten in Boletin de la Sociedad Matemática Mexicana New York [u.a.] : Springer International, 2014 25(2017), 1 vom: 16. Nov., Seite 131-144 (DE-627)779395166 (DE-600)2757902-5 2296-4495 nnns volume:25 year:2017 number:1 day:16 month:11 pages:131-144 https://dx.doi.org/10.1007/s40590-017-0188-0 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 16 11 131-144 |
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10.1007/s40590-017-0188-0 doi (DE-627)SPR036692050 (SPR)s40590-017-0188-0-e DE-627 ger DE-627 rakwb eng Jimenez-Lopez, Francisco G. verfasserin aut On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Matemática Mexicana 2017 Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. Asymptotic length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum metric (dpeaa)DE-He213 Surfaces of infinite type (dpeaa)DE-He213 Enthalten in Boletin de la Sociedad Matemática Mexicana New York [u.a.] : Springer International, 2014 25(2017), 1 vom: 16. Nov., Seite 131-144 (DE-627)779395166 (DE-600)2757902-5 2296-4495 nnns volume:25 year:2017 number:1 day:16 month:11 pages:131-144 https://dx.doi.org/10.1007/s40590-017-0188-0 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 16 11 131-144 |
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10.1007/s40590-017-0188-0 doi (DE-627)SPR036692050 (SPR)s40590-017-0188-0-e DE-627 ger DE-627 rakwb eng Jimenez-Lopez, Francisco G. verfasserin aut On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Matemática Mexicana 2017 Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. Asymptotic length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum metric (dpeaa)DE-He213 Surfaces of infinite type (dpeaa)DE-He213 Enthalten in Boletin de la Sociedad Matemática Mexicana New York [u.a.] : Springer International, 2014 25(2017), 1 vom: 16. Nov., Seite 131-144 (DE-627)779395166 (DE-600)2757902-5 2296-4495 nnns volume:25 year:2017 number:1 day:16 month:11 pages:131-144 https://dx.doi.org/10.1007/s40590-017-0188-0 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 16 11 131-144 |
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Jimenez-Lopez, Francisco G. |
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Jimenez-Lopez, Francisco G. misc Asymptotic length spectrum Teichmüller space misc Length spectrum Teichmüller space misc Length spectrum metric misc Surfaces of infinite type On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type |
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On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type Asymptotic length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum Teichmüller space (dpeaa)DE-He213 Length spectrum metric (dpeaa)DE-He213 Surfaces of infinite type (dpeaa)DE-He213 |
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misc Asymptotic length spectrum Teichmüller space misc Length spectrum Teichmüller space misc Length spectrum metric misc Surfaces of infinite type |
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misc Asymptotic length spectrum Teichmüller space misc Length spectrum Teichmüller space misc Length spectrum metric misc Surfaces of infinite type |
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On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type |
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On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type |
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Jimenez-Lopez, Francisco G. |
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Boletin de la Sociedad Matemática Mexicana |
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10.1007/s40590-017-0188-0 |
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on the completeness of the asymptotic length spectrum teichmüller space of surfaces of infinite type |
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On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type |
| abstract |
Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. © Sociedad Matemática Mexicana 2017 |
| abstractGer |
Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. © Sociedad Matemática Mexicana 2017 |
| abstract_unstemmed |
Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. We also prove that in this case, the space is homeomorphic to %$l^{\infty }/c_0%$, where %$l^{\infty }%$ is the Banach space of bounded sequences and %$c_0%$ is the subspace of sequences converging to zero. © Sociedad Matemática Mexicana 2017 |
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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">SPR036692050</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230328191647.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2017 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40590-017-0188-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR036692050</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40590-017-0188-0-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="100" ind1="1" ind2=" "><subfield code="a">Jimenez-Lopez, Francisco G.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the completeness of the asymptotic length spectrum Teichmüller space of surfaces of infinite type</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</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="500" ind1=" " ind2=" "><subfield code="a">© Sociedad Matemática Mexicana 2017</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The length spectrum Teichmüller space %$T_{ls}(R)%$, based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in %$T_{ls}(R)%$ are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space %$AT_{ls}(R)%$. In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then %$AT_{ls}(R)%$ is complete under the natural metric. 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