{"title":"Prescribed non-positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation","authors":"Romain Gicquaud","doi":"10.4310/cag.2023.v31.n8.a6","DOIUrl":null,"url":null,"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 [$\\href{https://dx.doi.org/10.4310/CAG.2018.v26.n5.a5}{14}$, $\\href{https://doi.org/10.1090/S0002-9947-1995-1321588-5}{26}$], we obtain a necessary and sufficient condition on the zero set of the prescribed scalar curvature so that the problem admits a (unique) solution.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"27 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2023.v31.n8.a6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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 [$\href{https://dx.doi.org/10.4310/CAG.2018.v26.n5.a5}{14}$, $\href{https://doi.org/10.1090/S0002-9947-1995-1321588-5}{26}$], we obtain a necessary and sufficient condition on the zero set of the prescribed scalar curvature so that the problem admits a (unique) solution.
期刊介绍：
Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
