4 citations · 6 across the 8 of their papers we have counts for
8 papers
Dual volume approximation of the Euclidean ball by polytopes with a fixed number of -faces
Steven Hoehner, Carsten Schütt, Elisabeth M. Werner
We study dual volume approximation of the Euclidean ball by polytopes with a prescribed number of -dimensional faces. This continues the authors' previous work on intrinsic volu…
Expected extremal area of facets of random polytopes
Brett Leroux, Luis Rademacher, Carsten Schütt +1
We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in . The extremal properties of int…
Spherical convex hull of random points on a wedge
Florian Besau, Anna Gusakova, Matthias Reitzner +3
Consider two half-spaces and in whose bounding hyperplanes and are orthogonal and pass through the origin. The intersection $\mathbb{…
Affine invariant maps for log-concave functions
Ben Li, Carsten Schütt, Elisabeth M. Werner
Affine invariant points and maps for sets were introduced by Grünbaum to study the symmetry structure of convex sets. We extend these notions to a functional setting. The role of s…
Constrained convex bodies with extremal affine surface areas
O. Giladi, H. Huang, C. Schütt +1
Given a convex body K in R^n and p in R, we introduce and study the extremal inner and outer affine surface areas IS_p(K) = sup_{K'\subseteq K} (as_p(K') ) and os_p(K)=inf_{K'\sups…
The Loewner function of a log-concave function
Ben Li, Carsten Schuett, Elisabeth M. Werner
We introduce the notion of Loewner (ellipsoid) function for a log concave function and show that it is an extension of the Loewner ellipsoid for convex bodies. We investigate its d…
Functional versions of L_p-affine surface area and entropy inequalities
U. Caglar, M. Fradelizi, O. Guedon +3
In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the…
Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
S. Artstein-Avidan, B. Klartag, C. Schuett +1
We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality inequa…