A longstanding question in the dual Brunn–Minkowski theory is “What are the dual
analogues of Federer's curvature measures for convex bodies?” The answer to this is …

During the past two decades the notion of affine surface area (from affine differential
geometry) and the isoperimetric inequalities related to it, have attracted increased interest …

The logarithmic Minkowski problem Page 1 JOURNAL OF THE AMERICAN MATHEMATICAL
SOCIETY Volume 26, Number 3, July 2013, Pages 831–852 S 0894-0347(2012)00741-3 …

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 Lp-Minkowski problem introduced by Lutwak is solved for p⩾ n+ 1 in the smooth
category. The relevant Monge–Ampère equation (0.1) is solved for all p> 1. The same …

A sharp affine Lp Sobolev inequality for functions on Euclidean n-space is established. This
new inequality is significantly stronger than (and directly implies) the classical sharp Lp …

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 …

Gauss curvature flow: the fate of the rolling stones Page 1 Digital Object Identifier (DOI)
10.1007/s002229900004 Invent. math. 138, 151–161 (1999) © Springer-Verlag 1999 …