# New integral estimates in substatic Riemannian manifolds and the Alexandrov Theorem

created by pinamonti on 10 May 2021

[BibTeX]

Preprint

Inserted: 10 may 2021
Last Updated: 10 may 2021

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.