Anisotropic $p$-capacity and anisotropic Minkowski inequality

Abstract

In this paper, we prove a sharp anisotropic $L^p$ Minkowski inequality involving the total $L^p$ anisotropic mean curvature and the anisotropic $p$-capacity, for any bounded domains with smooth boundary in ${\mathbb{R}}^n$. As consequences, we obtain an anisotropic Willmore inequality, a sharp anisotropic Minkowski inequality for outward $F$-minimising sets and a sharp volumetric anisotropic Minkowski inequality. For the proof, we utilize a nonlinear potential theoretic approach which has been recently developed in \cite{AFM1}.

it has been accepted for publication in SCIENCE CHINA Mathematics

References in corpus (6)

• On the mass of static metrics with positive cosmological constant - I
• Quantum reverse hypercontractivity: its tensorization and application to strong converses
• On the mass of static metrics with positive cosmological constant -- II
• The Brunn-Minkowski inequality and a Minkowski problem for $\mathcal{A}$-harmonic Green's function
• Motion of level sets by inverse anisotropic mean curvature
• Symmetrization with respect to mixed volumes

Cited by in corpus (1)

• A Green's function proof of the Positive Mass Theorem