Communications in Analysis and Geometry

Volume 26 (2018)

Number 2

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

Pages: 435 – 460

DOI: https://dx.doi.org/10.4310/CAG.2018.v26.n2.a6

Authors

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

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

Abstract

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.

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

Received 22 September 2015

Published 7 May 2018