A description of continuous rigid motion compatible Minkowski valuations is established. As an application we present a Brunn–Minkowski type inequality for intrinsic volumes of these valuations.

We prove a functional version of the Brunn-Minkowski inequality for restricted sums obtained by Szarek and Voicu-lescu. We only consider Lebesgue-measurable subsets of R n , and for A ⊂ R n , we denote its volume by |A|. If A, B ⊂ R n , their Minkowski sum is defined by A + B = {x + y, (x, y) ∈ A × B}. The classical Brunn-Minkowski inequality provides a lower bound for its volume. In their stud...

Week 1 (9/7/2010) . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Basic Results and Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Existence of Haar Measure . . . . . . . . . . . . . . . . . . . . . . . . . ...

We derive a Brunn-Minkowski-type inequality regarding the volume of the Minkowski sum of degenerate sets, namely, line sets. Let A 1 : : : A n be one dimensional sets of unit length, and v

Abstract. A generalization of Young’s inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified proof of recent entropy power inequalities of Barron and Madiman, as well as of a (conjectured) generalization of the Brunn-Minkowski inequality. ...

We present an argument which leads from the Brunn-Minkowski inequality to a Poincaré type inequality on the boundary of a convex body K of class C + in R . We prove that for every ψ ∈ C(∂K)

For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn-Minkowski inequality and a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality. It is shown that these two families of inequalities are “equiv...