Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)

Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)

In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R  ≥ − n ( n − 1) and also the rigidity result wh...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Annales Henri Poincaré 2016-04, Vol.17 (4), p.953-977
Hauptverfasser: Hu, Xue, Ji, Dandan, Shi, Yuguang
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Curvature
Dynamical Systems and Ergodic Theory
Elementary Particles
Flow stability
Manifolds
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 977
container_issue 4
container_start_page 953
container_title Annales Henri Poincaré
container_volume 17
creator Hu, Xue
Ji, Dandan
Shi, Yuguang
description In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R  ≥ − n ( n − 1) and also the rigidity result when certain relative volume is zero.
doi_str_mv 10.1007/s00023-015-0411-3
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2343277387</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2343277387</sourcerecordid><originalsourceid>FETCH-LOGICAL-c359t-ee303a1b46442f4ad75b0f489453e43c4662d8d86ab6f439edc87c78f05e386d3</originalsourceid><addsrcrecordid>eNp1kM1KxDAUhYsoOI4-gLuAG11Uk9w0SZdS_IMRwb-lIdMmWmmbMWmVeQPd-gRufBEfZZ7EDhVduTr3cs85F74o2iZ4n2AsDgLGmEKMSRJjRkgMK9GIMMpizDlZ_Z1BrEcbITxiTKiEdBTd3bqqqw3KXD3TvgyuQc72W2Odr3VVzYdL3qJz3ZTWVUVAL2X7gK5yXWmPss4_67bzBl1-fSzePtHi9b1Bu81SEdnbjNasroLZ-tFxdHN8dJ2dxpOLk7PscBLnkKRtbAxg0GTKOGPUMl2IZIotkylLwDDIGee0kIXkesotg9QUuRS5kBYnBiQvYBztDL0z7546E1r16Drf9C8VBQZUCJCid5HBlXsXgjdWzXxZaz9XBKslRjVgVD1GtcSooM_QIRN6b3Nv_F_z_6Fv68p25Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2343277387</pqid></control><display><type>article</type><title>Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)</title><source>SpringerNature Journals</source><creator>Hu, Xue ; Ji, Dandan ; Shi, Yuguang</creator><creatorcontrib>Hu, Xue ; Ji, Dandan ; Shi, Yuguang</creatorcontrib><description>In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R  ≥ − n ( n − 1) and also the rigidity result when certain relative volume is zero.</description><identifier>ISSN: 1424-0637</identifier><identifier>EISSN: 1424-0661</identifier><identifier>DOI: 10.1007/s00023-015-0411-3</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Classical and Quantum Gravitation ; Curvature ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Flow stability ; Manifolds ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Physics ; Physics and Astronomy ; Quantum Field Theory ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Annales Henri Poincaré, 2016-04, Vol.17 (4), p.953-977</ispartof><rights>Springer Basel 2015</rights><rights>2015© Springer Basel 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-ee303a1b46442f4ad75b0f489453e43c4662d8d86ab6f439edc87c78f05e386d3</citedby><cites>FETCH-LOGICAL-c359t-ee303a1b46442f4ad75b0f489453e43c4662d8d86ab6f439edc87c78f05e386d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00023-015-0411-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00023-015-0411-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Hu, Xue</creatorcontrib><creatorcontrib>Ji, Dandan</creatorcontrib><creatorcontrib>Shi, Yuguang</creatorcontrib><title>Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)</title><title>Annales Henri Poincaré</title><addtitle>Ann. Henri Poincaré</addtitle><description>In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R  ≥ − n ( n − 1) and also the rigidity result when certain relative volume is zero.</description><subject>Classical and Quantum Gravitation</subject><subject>Curvature</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Flow stability</subject><subject>Manifolds</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KxDAUhYsoOI4-gLuAG11Uk9w0SZdS_IMRwb-lIdMmWmmbMWmVeQPd-gRufBEfZZ7EDhVduTr3cs85F74o2iZ4n2AsDgLGmEKMSRJjRkgMK9GIMMpizDlZ_Z1BrEcbITxiTKiEdBTd3bqqqw3KXD3TvgyuQc72W2Odr3VVzYdL3qJz3ZTWVUVAL2X7gK5yXWmPss4_67bzBl1-fSzePtHi9b1Bu81SEdnbjNasroLZ-tFxdHN8dJ2dxpOLk7PscBLnkKRtbAxg0GTKOGPUMl2IZIotkylLwDDIGee0kIXkesotg9QUuRS5kBYnBiQvYBztDL0z7546E1r16Drf9C8VBQZUCJCid5HBlXsXgjdWzXxZaz9XBKslRjVgVD1GtcSooM_QIRN6b3Nv_F_z_6Fv68p25Q</recordid><startdate>20160401</startdate><enddate>20160401</enddate><creator>Hu, Xue</creator><creator>Ji, Dandan</creator><creator>Shi, Yuguang</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160401</creationdate><title>Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)</title><author>Hu, Xue ; Ji, Dandan ; Shi, Yuguang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-ee303a1b46442f4ad75b0f489453e43c4662d8d86ab6f439edc87c78f05e386d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Curvature</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Flow stability</topic><topic>Manifolds</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Xue</creatorcontrib><creatorcontrib>Ji, Dandan</creatorcontrib><creatorcontrib>Shi, Yuguang</creatorcontrib><collection>CrossRef</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Xue</au><au>Ji, Dandan</au><au>Shi, Yuguang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. Henri Poincaré</stitle><date>2016-04-01</date><risdate>2016</risdate><volume>17</volume><issue>4</issue><spage>953</spage><epage>977</epage><pages>953-977</pages><issn>1424-0637</issn><eissn>1424-0661</eissn><abstract>In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R  ≥ − n ( n − 1) and also the rigidity result when certain relative volume is zero.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00023-015-0411-3</doi><tpages>25</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1424-0637
ispartof Annales Henri Poincaré, 2016-04, Vol.17 (4), p.953-977
issn 1424-0637
1424-0661
language eng
recordid cdi_proquest_journals_2343277387
source SpringerNature Journals
subjects Classical and Quantum Gravitation
Curvature
Dynamical Systems and Ergodic Theory
Elementary Particles
Flow stability
Manifolds
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
title Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-18T20%3A53%3A41IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Volume%20Comparison%20of%20Conformally%20Compact%20Manifolds%20with%20Scalar%20Curvature%20R%C2%A0%E2%89%A5%20%E2%88%92n%20(n%20%E2%88%92%201)&rft.jtitle=Annales%20Henri%20Poincar%C3%A9&rft.au=Hu,%20Xue&rft.date=2016-04-01&rft.volume=17&rft.issue=4&rft.spage=953&rft.epage=977&rft.pages=953-977&rft.issn=1424-0637&rft.eissn=1424-0661&rft_id=info:doi/10.1007/s00023-015-0411-3&rft_dat=%3Cproquest_cross%3E2343277387%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2343277387&rft_id=info:pmid/&rfr_iscdi=true