We establish dual equivalent forms involving relative entropy, Fisher information, and
optimal transport costs of inverse Santaló inequalities. We show in particular that the Mahler …

Our purpose here is to give an overview of known results and open questions concerning
the volume product 𝒫 (K)= minz∈ K vol (K) vol ((K− z)∗) of a convex body K in ℝn. We …

It is shown that each monotone Minkowski endomorphism of convex bodies gives rise to an
isoperimetric inequality, which directly implies the classical Urysohn inequality. Among this …

We study the normalized volume of toric singularities. As it turns out, there is a close relation
to the notion of (nonsymmetric) Mahler volume from convex geometry. This observation …

The goal of this paper is to study geometric and extremal properties of the convex body BF
(M), which is the unit ball of the Lipschitz-free Banach space associated with a finite metric …

Our main contribution is a concentration inequality for the symmetric volume difference of a
C^ 2 C 2 convex body with positive Gaussian curvature and a circumscribed random …

We investigate weighted floating bodies of polytopes. We show that the weighted volume
depends on the complete flags of the polytope. This connection is obtained by introducing …

In recent years, it has been shown that some classical inequalities follow from a local
stochastic dominance for naturally associated random polytopes. We strengthen planar …

Volume of geometric objects plays an important role in applied and theoretical mathematics.
This is particularly true in the relatively new branch of discrete geometry, where volume is …

Abstract The Blaschke–Santaló inequality is a classical inequality in convex geometry
concerning the volume of a convex body and that of its dual. In this work we investigate an …