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 study of the geometry of convex bodies based on information about sections and
projections of these bodies has important applications in many areas of mathematics and …

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) …

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 …

Two new approaches are presented to establish the existence of polytopal solutions to the
discrete-data Lp Minkowski problem for all p> 1. As observed by Schneider [23], the Brunn …

It is shown that the classical John ellipsoid, the Petty ellipsoid and a recently discovered
'dual'of the Legendre ellipsoid are all special cases (ellipsoids which can be associated with …

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 …

Abstract An affine Moser–Trudinger inequality, which is stronger than the Euclidean Moser–
Trudinger inequality, is established. In this new affine analytic inequality an affine energy of …