Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation
We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the case of asymptotically hyperbolic manifolds and restrict ourselves to non positive prescribed scalar curvature. Following e...
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| creator | Gicquaud, Romain |
| description | We study the prescribed scalar curvature problem, namely finding which
function can be obtained as the scalar curvature of a metric in a given
conformal class. We deal with the case of asymptotically hyperbolic manifolds
and restrict ourselves to non positive prescribed scalar curvature. Following
earlier results, we obtain a necessary and sufficient condition on the zero set
of the prescribed scalar curvature so that the problem admits a (unique)
solution. |
| doi_str_mv | 10.48550/arxiv.1909.05343 |
| format | Article |
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function can be obtained as the scalar curvature of a metric in a given
conformal class. We deal with the case of asymptotically hyperbolic manifolds
and restrict ourselves to non positive prescribed scalar curvature. Following
earlier results, we obtain a necessary and sufficient condition on the zero set
of the prescribed scalar curvature so that the problem admits a (unique)
solution.</description><identifier>DOI: 10.48550/arxiv.1909.05343</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs ; Mathematics - Differential Geometry ; Physics - General Relativity and Quantum Cosmology</subject><creationdate>2019-09</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1909.05343$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1909.05343$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Gicquaud, Romain</creatorcontrib><title>Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation</title><description>We study the prescribed scalar curvature problem, namely finding which
function can be obtained as the scalar curvature of a metric in a given
conformal class. We deal with the case of asymptotically hyperbolic manifolds
and restrict ourselves to non positive prescribed scalar curvature. Following
earlier results, we obtain a necessary and sufficient condition on the zero set
of the prescribed scalar curvature so that the problem admits a (unique)
solution.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Differential Geometry</subject><subject>Physics - General Relativity and Quantum Cosmology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotkM9qhDAYxHPpoWz7AD01L6CNRqM5lqX_QGgPe5cv8RMDamwS3Vrou9faPQ3MjxmYIeQuYXFW5jl7APdlljiRTMYs5xm_Jj8fDr12RmFDRzvSyXoTzILUa-jBUT27BcLskG4Q_DpMwQazsX6l3TqhU7Y3mg4wmtb2jadnEzoK07S5EMwWCpaGDmlldDeis2ejvyl-zju8IVct9B5vL3ogp-en0_E1qt5f3o6PVQSi4BEWjUYmE4kcZcYzyBslkKtUiFJJAGiF0oVIQCsmQMl2WyZUU-aQsbRIc34g9_-1-_56cmYAt9Z_P9T7D_wXDLtdAw</recordid><startdate>20190911</startdate><enddate>20190911</enddate><creator>Gicquaud, Romain</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190911</creationdate><title>Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation</title><author>Gicquaud, Romain</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-e7dce0919e3e9434a5db6e3b2668b9aaaf6bc761acb06ab9f3436bd85a4027253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Differential Geometry</topic><topic>Physics - General Relativity and Quantum Cosmology</topic><toplevel>online_resources</toplevel><creatorcontrib>Gicquaud, Romain</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Gicquaud, Romain</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation</atitle><date>2019-09-11</date><risdate>2019</risdate><abstract>We study the prescribed scalar curvature problem, namely finding which
function can be obtained as the scalar curvature of a metric in a given
conformal class. We deal with the case of asymptotically hyperbolic manifolds
and restrict ourselves to non positive prescribed scalar curvature. Following
earlier results, we obtain a necessary and sufficient condition on the zero set
of the prescribed scalar curvature so that the problem admits a (unique)
solution.</abstract><doi>10.48550/arxiv.1909.05343</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Differential Geometry Physics - General Relativity and Quantum Cosmology |
| title | Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation |
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