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

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2024-08-10 DOI:10.4310/cag.2023.v31.n8.a6

Romain Gicquaud

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引用次数: 0

摘要

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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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 [$\href{https://dx.doi.org/10.4310/CAG.2018.v26.n5.a5}{14}$, $\href{https://doi.org/10.1090/S0002-9947-1995-1321588-5}{26}$], we obtain a necessary and sufficient condition on the zero set of the prescribed scalar curvature so that the problem admits a (unique) solution.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

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.