Calculus of Variations and Geometric Measure Theory
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L. Benatti - M. Fogagnolo - L. Mazzieri

Minkowski Inequality on complete Riemannian manifolds with nonnegative Ricci curvature

created by benatti on 21 Jan 2021
modified on 14 Jun 2021

[BibTeX]

preprint

Inserted: 21 jan 2021
Last Updated: 14 jun 2021

Year: 2021

ArXiv: 2101.06063 PDF

Abstract:

In this paper we consider Riemannian manifolds of dimension at least 3, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we prove the validity of a new optimal Minkowski Inequality. Along with the proof, we establish sharp monotonicity formulas, holding along the level sets of p-capacitary potentials in p-nonparabolic manifolds with nonnegative Ricci curvature.

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