The Brunn-minkowski Inequality: Work in Progress

The Brunn-Minkowski-Type Inequality

Volume difference inequalities for the projection and intersection bodies

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

The Infinitesimal Form of Brunn-minkowski Type Inequalities

Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang [7], and it states that a certain strengthening of the classical Brunn-Minkowski inequality is admissible in the case of symmetric convex sets. It was recently shown by Nayar, Zvavitch, the second and the third authors [27], that Log-Brunn-Minkowski inequality implies a certain dimensional Brunn-Minkowski inequal...

The Brunn-Minkowski Inequality

In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of Rn, and deserves to be better known. This guide explains the relationship between the Brunn-Minkowski inequality and other inequalities in geometry and analysis, an...

Borell’s generalized Prékopa-Leindler inequality: A simple proof

We present a simple proof of Christer Borell’s general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell’s inequality to the log-Brunn-Minkowski inequality of Böröczky, Lutwak, Yang and Zhang.