Communications in Analysis and Geometry
Volume 26 (2018)
A unified treatment for $L_p$ Brunn-Minkowski type inequalities
Pages: 435 – 460
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