Prescribed non-positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation

IF 0.7 4区 数学 Q2 MATHEMATICS
Romain Gicquaud
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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.
渐近双曲流形上的规定非正标量曲率与利希诺维奇方程的应用
我们研究的是规定标量曲率问题,即在给定的共形类中,找到哪个函数可以作为度量的标量曲率。我们处理的是渐近双曲流形的情况,并把自己限制在非正的规定标量曲率上。继[$\href{https://dx.doi.org/10.4310/CAG.2018.v26.n5.a5}{14}$, $\href{https://doi.org/10.1090/S0002-9947-1995-1321588-5}{26}$]之后,我们得到了关于规定标量曲率零集的必要条件和充分条件,这样问题就有了(唯一的)解。
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
4
审稿时长
>12 weeks
期刊介绍: Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.
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