Minkowski Inequality on complete Riemannian manifolds with nonnegative Ricci curvature
Abstract
In this paper we consider Riemannian manifolds of dimension at least , with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski Inequality. We also characterise the equality case, provided the domain is strictly outward minimising and strictly mean convex. Along with the proof, we establish in full generality sharp monotonicity formulas, holding along the level sets of -capacitary potentials in -nonparabolic manifolds with nonnegative Ricci curvature.
Keywords
Cite
@article{arxiv.2101.06063,
title = {Minkowski Inequality on complete Riemannian manifolds with nonnegative Ricci curvature},
author = {Luca Benatti and Mattia Fogagnolo and Lorenzo Mazzieri},
journal= {arXiv preprint arXiv:2101.06063},
year = {2024}
}
Comments
The asymptotically conical assumption has been removed using a different technique. Since the study of the asymptotic behaviour of the p-capacitary potential is no more necessary, we decided to omit it for brevity's sake, but it can be found in v3