The quermassintegral inequalities for starshaped domains

TL;DR

This paper provides a straightforward proof of the isoperimetric inequality for quermassintegrals in non-convex starshaped domains, leveraging recent results on geometric curvature flows.

Contribution

It introduces a simple proof technique for quermassintegral inequalities in starshaped domains using curvature flow results, extending previous convex domain results.

Findings

Proof of isoperimetric inequality for non-convex starshaped domains

Application of curvature flow results to geometric inequalities

Extension of classical inequalities to broader domain classes

Abstract

We give a simple proof of the insoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a reslut of Gerhardt \cite{G} and Urbas \cite{U} on an expanding geometric curvature flow.