A unified treatment for Lp Brunn-Minkowski type inequalities

TL;DR

This paper refines a unified approach called the Lp transference principle to generalize classical Brunn-Minkowski inequalities to the Lp setting, leading to new inequalities involving mixed volume, inertia, and other geometric measures.

Contribution

The paper introduces a refined Lp transference principle that unifies and extends classical inequalities to the Lp context, establishing several new inequalities in convex geometry.

Findings

New Lp Brunn-Minkowski inequalities for mixed volume and inertia.

Effective demonstration of the Lp transference principle's applicability.

Establishment of inequalities involving quermassintegral, projection body, and capacity.

Abstract

A unified approach used to generalize classical Brunn-Minkowski type inequalities to Lp Brunn-Minkowski type inequalities, called the Lp transference principle, is refined in this paper. As illustrations of the effectiveness and practicability of this method, several new Lp Brunn-Minkowski type inequalities concerning the mixed volume, moment of inertia, quermassintegral, projection body and capacity are established.