Neumann Isoperimetric Constant Estimate for Convex Domains

TL;DR

This paper provides a new, direct proof of the local Neumann isoperimetric inequality specifically for convex domains within Riemannian manifolds that have Ricci curvature bounded below, enhancing understanding of geometric inequalities.

Contribution

It introduces a novel, direct proof method for the Neumann isoperimetric inequality applicable to convex domains in curved spaces.

Findings

Establishes a new proof technique for isoperimetric inequalities.

Applicable to convex domains with Ricci curvature bounds.

Strengthens theoretical understanding of geometric inequalities.

Abstract

We present a new and direct proof of the local Neumann isoperimetric inequality on convex domains of a Riemannian manifold with Ricci curvature bounded below.