Anisotropic Isoperimetric Inequality outside Euclidean Ball

TL;DR

This paper establishes a sharp anisotropic isoperimetric inequality for domains outside Euclidean balls in higher-dimensional spaces using the ABP method applied to a Neumann boundary value problem.

Contribution

It introduces a novel anisotropic isoperimetric inequality for exterior domains outside Euclidean balls, employing the ABP method in a new context.

Findings

Proves a sharp anisotropic isoperimetric inequality for exterior domains.

Applies the ABP method to a Neumann boundary value problem in this setting.

Extends classical isoperimetric results to anisotropic and exterior domain cases.

Abstract

We prove an sharp anisotropic isoperimetric inequality for a domain outside an Euclidean ball in $\mathbb{R}^n$ for $n\geq 2$. The proof applies the ABP method to a Neumann boundary value problem.