Calculus of Variations and Geometric Measure Theory

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 20 Jul 2023


Accepted Paper

Inserted: 21 jan 2021
Last Updated: 20 jul 2023

Journal: Analysis & PDE
Year: 2021

ArXiv: 2101.06063 PDF


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 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 $p$-capacitary potentials in $p$-nonparabolic manifolds with nonnegative Ricci curvature.