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 …

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 …

General affine surface areas Page 1 Advances in Mathematics 224 (2010) 2346–2360 www.elsevier.com/locate/aim
General affine surface areas Monika Ludwig1 Department of Mathematics, Polytechnic …

Chord measures are newly discovered translation-invariant geometric measures of convex
bodies in R n, in addition to Aleksandrov-Fenchel-Jessen's area measures. They are …

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 …

On the Lp Monge–Ampère equation - ScienceDirect Skip to main contentSkip to article
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The centro-affine Minkowski problem, a critical case of the L_p L p-Minkowski problem in the
n+ 1 n+ 1 dimensional Euclidean space is considered. By applying methods of calculus of …

We show that the fundamental objects of the Lp-Brunn–Minkowski theory, namely the Lp-
affine surface areas for a convex body, are closely related to information theory: they are …