Calculus of Variations and Geometric Measure Theory

M. Fogagnolo - A. Pinamonti

New integral estimates in substatic Riemannian manifolds and the Alexandrov Theorem

created by pinamonti on 10 May 2021
modified on 25 Apr 2022

[BibTeX]

Accepted Paper

Inserted: 10 may 2021
Last Updated: 25 apr 2022

Journal: J. Math. Pures Appl.
Year: 2021

Abstract:

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 leading to the Alexandrov Theorem in $\R^n$ and improve on a Heintze-Karcher type inequality due to Li-Xia. Our method relies on the introduction of a new vector field with nonnegative divergence, generalizing to this setting the P-function technique of Weinberger.


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