Communications in Analysis and Geometry

Volume 26 (2018)

Number 2

A unified treatment for $L_p$ Brunn-Minkowski type inequalities

Pages: 435 – 460



Du Zou (Department of Mathematics, Wuhan University of Science and Technology, Wuhan, China)

Ge Xiong (School of Mathematical Sciences, Tongji University, Shanghai, China)


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

Research of the authors was supported by NSFC No. 11471206 and No. 11601399.

Received 22 September 2015

Published 7 May 2018