Ideal polyhedral surfaces in Fuchsian manifolds
Let $S_{g,n}$ be a surface of genus $g > 1$ with $n>0$ punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an altern...
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| creator | Prosanov, Roman |
| description | Let $S_{g,n}$ be a surface of genus $g > 1$ with $n>0$ punctures equipped
with a complete hyperbolic cusp metric. Then it can be uniquely realized as the
boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a
new variational proof of this result. We also give an alternative proof of the
existence and uniqueness of a hyperbolic polyhedral metric with prescribed
curvature in a given conformal class. |
| doi_str_mv | 10.48550/arxiv.1804.05893 |
| format | Article |
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with a complete hyperbolic cusp metric. Then it can be uniquely realized as the
boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a
new variational proof of this result. We also give an alternative proof of the
existence and uniqueness of a hyperbolic polyhedral metric with prescribed
curvature in a given conformal class.</description><identifier>DOI: 10.48550/arxiv.1804.05893</identifier><language>eng</language><subject>Mathematics - Geometric Topology ; Mathematics - Metric Geometry</subject><creationdate>2018-04</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1804.05893$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1804.05893$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Prosanov, Roman</creatorcontrib><title>Ideal polyhedral surfaces in Fuchsian manifolds</title><description>Let $S_{g,n}$ be a surface of genus $g > 1$ with $n>0$ punctures equipped
with a complete hyperbolic cusp metric. Then it can be uniquely realized as the
boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a
new variational proof of this result. We also give an alternative proof of the
existence and uniqueness of a hyperbolic polyhedral metric with prescribed
curvature in a given conformal class.</description><subject>Mathematics - Geometric Topology</subject><subject>Mathematics - Metric Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrsKwjAYhuEsDqJegJO9gdb8TWKSUcQTCC7dy98caKCtkqDo3Xucvnf6eAiZAy24EoIuMT7CvQBFeUGF0mxMlkfrsMuul-7ZOhvfmW7Ro3EpC0O2u5k2BRyyHofgL51NUzLy2CU3---EVLtttTnkp_P-uFmfclxJltvScQMWOGjtGqZ046XQAuQKmW6olGXJNTJkXokSwMlGaWsMUCWk5MqyCVn8br_i-hpDj_FZf-T1V85ewYs8vw</recordid><startdate>20180416</startdate><enddate>20180416</enddate><creator>Prosanov, Roman</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20180416</creationdate><title>Ideal polyhedral surfaces in Fuchsian manifolds</title><author>Prosanov, Roman</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-d2e4c1d14199eb389bf7595176a39b0772249a3a3f85211e7b89dcc10857748d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Mathematics - Geometric Topology</topic><topic>Mathematics - Metric Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Prosanov, Roman</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Prosanov, Roman</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Ideal polyhedral surfaces in Fuchsian manifolds</atitle><date>2018-04-16</date><risdate>2018</risdate><abstract>Let $S_{g,n}$ be a surface of genus $g > 1$ with $n>0$ punctures equipped
with a complete hyperbolic cusp metric. Then it can be uniquely realized as the
boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a
new variational proof of this result. We also give an alternative proof of the
existence and uniqueness of a hyperbolic polyhedral metric with prescribed
curvature in a given conformal class.</abstract><doi>10.48550/arxiv.1804.05893</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Geometric Topology Mathematics - Metric Geometry |
| title | Ideal polyhedral surfaces in Fuchsian manifolds |
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