New integral estimates in substatic Riemannian manifolds and the Alexandrov Theorem

被引：7

作者：

Fogagnolo, Mattia ^{[1
]}

Pinamonti, Andrea ^{[2
]}

机构：

[1] Scuola Normale Super Pisa, Ctr Ric Matemat Ennio Giorgi, Piazza Cavalieri 3, I-56126 Pisa, Italy

[2] Univ Trento, Via Sommar 14, I-38123 Povo, TN, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2022年 / 163卷

关键词：

Alexandrov Theorem; Heintze-Karcher inequality; Substatic manifolds; Boundary value problem; CONSTANT MEAN-CURVATURE; FORMULA; HYPERSURFACES; STABILITY;

D O I：

10.1016/j.matpur.2022.05.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive new integral estimates on substatic manifolds with boundary of horizon type, naturally arising in General Relativity. In particular, we generalize to this setting an identity due to Magnanini-Poggesi [24] leading to the Alexandrov Theorem in R-n and improve on a Heintze-Karcher type inequality due to Li-Xia [22]. Our method relies on the introduction of a new vector field with nonnegative divergence, generalizing to this setting the P-function technique of Weinberger [36]. (C) 2022 Elsevier Masson SAS. All rights reserved.

引用

页码：299 / 317

页数：19

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