Jesús Yepes Nicolás

On Brunn–Minkowski-Type Inequalities for Polar Bodies

In this paper we prove a Brunn–Minkowski-type inequality for the polar set of the

On a linear refinement of the Prekopa-leindler inequality

p

On the roots of generalized Wills

p-sum of convex bodies, which generalizes previous results by Firey, and we show it has an equivalent multiplicative version. We also make some considerations for the polar set of the so-called difference body.

\mu

The Brunn-Minkowski inequality asserts that the n-th root of the functional volume is concave, namely, vol((1 − λ)A + λB)1/n is greater than (1 − λ)vol(A)1/n + λvol(B)1/n for compact sets A, B and λ ∈ [0, 1]. Here we will show that if a given measure satisfies an inequality like this, with a certain positive power, for the family of all Euclidean balls then it must be a constant multiple of the volume.