For origin-symmetric convex bodies (ie, 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 …

The even Orlicz Minkowski problem Page 1 Advances in Mathematics 224 (2010) 2485–2510
www.elsevier.com/locate/aim The even Orlicz Minkowski problem Christoph Haberl, Erwin …

GENERAL Lp AFFINE ISOPERIMETRIC INEQUALITIES Christoph Haberl & Franz E.
Schuster Abstract 1. Introduction Projection bodies Page 1 j. differential geometry 83 (2009) …

A classification of upper semicontinuous and SL (n) invariant valuations on the space of n-
dimensional convex bodies is established. As a consequence, complete characterizations of …

The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a
star body (from below) by the volume of the star body itself is the Busemann-Petty centroid …

Minkowski's projection bodies have evolved into Lp projection bodies and their asymmetric
analogs. These all turn out to be part of a far larger class of Orlicz projection bodies. The …

Centroid and difference bodies define $\operatorname {SL}(n) $ equivariant operators on
convex bodies and these operators are valuations with respect to Minkowski addition. We …

Asymmetric affine Lp Sobolev inequalities Page 1 Journal of Functional Analysis 257 (2009)
641–658 www.elsevier.com/locate/jfa Asymmetric affine Lp Sobolev inequalities Christoph …

Abstract The Orlicz Brunn–Minkowski theory originated with the work of Lutwak, Yang, and
Zhang in 2010. In this paper, we first introduce the Orlicz addition of convex bodies …

All upper semicontinuous and $\mathrm {SL}(n) $ invariant valuations on convex bodies
containing the origin in their interiors are completely classified. Each such valuation is …