4 citations · 6 across the 8 of their papers we have counts for
8 papers
Illumination bodies for ball-convex bodies
Brandon Oliva, Elisabeth M. Werner, Diliya Yalikun
We introduce illumination bodies and weighted illumination bodies in the class of -dimensional -ball convex bodies. These bodies may be regarded as dual counterparts of the r…
Illumination Bodies in Projective Geometries
Rotem Assouline, Florian Besau, Elisabeth M. Werner
We extend the notion of illumination bodies to Riemannian spaces of constant curvature and to projective Finsler geometries. We prove that the derivative of their volume defines a…
Ball-convex bodies and relative surface areas
Elisabeth M. Werner, Diliya Yalikun
We define new surface area measures for ball-convex bodies which we call relative surface areas. We show that those are rigid motion invariant valuations. We establish inequa…
Floating bodies for ball-convex bodies
Carsten Schuett, Elisabeth M Werner, Diliya Yalikun
We define floating bodies in the class of -dimensional ball-convex bodies. A right derivative of volume of these floating bodies leads to a surface area measure for ball-convex…
Affine surface area
Carsten Schuett, Elisabeth M. Werner
We give an overview of the affine surface area, its properties and its history.
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…
Mixed f-divergence and inequalities for log concave functions
Umut Caglar, Elisabeth M. Werner
Mixed -divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions…
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…