On the Gardner-Zvavitch conjecture: Symmetry in inequalities of Brunn-Minkowski type

Gaussian Brunn-minkowski Inequalities

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and is shown to be the best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed and proved to be true in some significant special cases. Th...

The Brunn-Minkowski-Type Inequality

Gaussian Brunn - Minkowski Inequalities Richard

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and shown to be best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed, and proved to be true in some significant special cases. Througho...

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...

Some new Brunn-Minkowski-type inequalities in convex bodies

The Brunn-Minkowski inequality theory plays an important role in a number of mathematical disciplines such as measure theory, crystallography, optimal control theory, functional analysis, and geometric convexity. It has many useful applications in combinatorics, stochastic geometry, and mathematical economics. In recent years, several authors including Ball [1, 2, 3], Bourgain and Lindenstrauss...