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Mass Rigidity for Hyperbolic Manifolds
We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality p 0 = p 1 2 + ⋯ + p n 2 holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16...
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| Published in: | Communications in mathematical physics 2020-06, Vol.376 (3), p.2329-2349 |
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| Main Authors: | , , |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c319t-c78ed1f1fb621266c35c9cf9d2a6b1d58a3b30727f6f2e1de10e32e04fd358fa3 |
| container_end_page | 2349 |
| container_issue | 3 |
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| container_title | Communications in mathematical physics |
| container_volume | 376 |
| creator | Huang, Lan-Hsuan Jang, Hyun Chul Martin, Daniel |
| description | We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality
p
0
=
p
1
2
+
⋯
+
p
n
2
holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16(1):1–2, 1998; Chruściel and Herzlich in Pac J Math 212(2):231–264, 2003; Min-Oo in Math Ann 285(4):527–539; 1989, Wang in J Differ Geom 57(2):273–299, 2001) or under special asymptotics (Andersson et al. in Ann. Henri Poincaré 9(1):1–33, 2008). |
| doi_str_mv | 10.1007/s00220-019-03623-0 |
| format | article |
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p
0
=
p
1
2
+
⋯
+
p
n
2
holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16(1):1–2, 1998; Chruściel and Herzlich in Pac J Math 212(2):231–264, 2003; Min-Oo in Math Ann 285(4):527–539; 1989, Wang in J Differ Geom 57(2):273–299, 2001) or under special asymptotics (Andersson et al. in Ann. Henri Poincaré 9(1):1–33, 2008).</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-019-03623-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Asymptotic properties ; Classical and Quantum Gravitation ; Complex Systems ; Manifolds ; Mathematical and Computational Physics ; Mathematical Physics ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Rigidity ; Theoretical</subject><ispartof>Communications in mathematical physics, 2020-06, Vol.376 (3), p.2329-2349</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-c78ed1f1fb621266c35c9cf9d2a6b1d58a3b30727f6f2e1de10e32e04fd358fa3</citedby><cites>FETCH-LOGICAL-c319t-c78ed1f1fb621266c35c9cf9d2a6b1d58a3b30727f6f2e1de10e32e04fd358fa3</cites><orcidid>0000-0002-8918-3071</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>Huang, Lan-Hsuan</creatorcontrib><creatorcontrib>Jang, Hyun Chul</creatorcontrib><creatorcontrib>Martin, Daniel</creatorcontrib><title>Mass Rigidity for Hyperbolic Manifolds</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality
p
0
=
p
1
2
+
⋯
+
p
n
2
holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16(1):1–2, 1998; Chruściel and Herzlich in Pac J Math 212(2):231–264, 2003; Min-Oo in Math Ann 285(4):527–539; 1989, Wang in J Differ Geom 57(2):273–299, 2001) or under special asymptotics (Andersson et al. in Ann. Henri Poincaré 9(1):1–33, 2008).</description><subject>Asymptotic properties</subject><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Manifolds</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Rigidity</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAURYMoWKt_wFVBcBd9L2nTdimDzggzCKLrkOZjyFDbmnQW_fdWK7hz8-7m3vPgEHKNcIcA5X0EYAwoYE2BC8YpnJAEc84o1ChOSQKAQLlAcU4uYjwAQM2ESMjtTsWYvfq9N36cMteHbDMNNjR963W2U513fWviJTlzqo326jdT8v70-Lba0O3L-nn1sKWaYz1SXVbWoEPXCIYzX_NC19rVhinRoCkqxRsOJSudcMyisQiWMwu5M7yonOIpuVm4Q-g_jzaO8tAfQze_lCyHUkCeF_ncYktLhz7GYJ0cgv9QYZII8tuHXHzI2Yf88THflPBlFOdyt7fhD_3P6gsf0GFS</recordid><startdate>20200601</startdate><enddate>20200601</enddate><creator>Huang, Lan-Hsuan</creator><creator>Jang, Hyun Chul</creator><creator>Martin, Daniel</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-8918-3071</orcidid></search><sort><creationdate>20200601</creationdate><title>Mass Rigidity for Hyperbolic Manifolds</title><author>Huang, Lan-Hsuan ; Jang, Hyun Chul ; Martin, Daniel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-c78ed1f1fb621266c35c9cf9d2a6b1d58a3b30727f6f2e1de10e32e04fd358fa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Asymptotic properties</topic><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Manifolds</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Rigidity</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, Lan-Hsuan</creatorcontrib><creatorcontrib>Jang, Hyun Chul</creatorcontrib><creatorcontrib>Martin, Daniel</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huang, Lan-Hsuan</au><au>Jang, Hyun Chul</au><au>Martin, Daniel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Mass Rigidity for Hyperbolic Manifolds</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2020-06-01</date><risdate>2020</risdate><volume>376</volume><issue>3</issue><spage>2329</spage><epage>2349</epage><pages>2329-2349</pages><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality
p
0
=
p
1
2
+
⋯
+
p
n
2
holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16(1):1–2, 1998; Chruściel and Herzlich in Pac J Math 212(2):231–264, 2003; Min-Oo in Math Ann 285(4):527–539; 1989, Wang in J Differ Geom 57(2):273–299, 2001) or under special asymptotics (Andersson et al. in Ann. Henri Poincaré 9(1):1–33, 2008).</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-019-03623-0</doi><tpages>21</tpages><orcidid>https://orcid.org/0000-0002-8918-3071</orcidid></addata></record> |
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| ispartof | Communications in mathematical physics, 2020-06, Vol.376 (3), p.2329-2349 |
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| language | eng |
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| subjects | Asymptotic properties Classical and Quantum Gravitation Complex Systems Manifolds Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Rigidity Theoretical |
| title | Mass Rigidity for Hyperbolic Manifolds |
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