Published Paper

Inserted: 21 jan 2021
Last Updated: 19 nov 2024

Journal: Analysis & PDE
Volume: 17
Number: 9
Year: 2024
Doi: 10.2140/apde.2024.17.3039

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 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.