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


Accepted Paper

Inserted: 10 may 2021
Last Updated: 25 apr 2022

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


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.