A Prékopa-Leindler type inequality of the $L_p$ Brunn-Minkowski inequality

Abstract

In this paper, we prove a Prékopa-Leindler type inequality of the $L_p$ Brunn-Minkowski inequality. It extends an inequality proved by Das Gupta [8] and Klartag [16], and thus recovers the Prékopa-Leindler inequality. In addition, we prove a functional $L_p$ Minkowski inequality.

References in corpus (1)

• On $L_p$-Brunn-Minkowski type and $L_p$-isoperimetric type inequalities for general measures