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 …

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 …

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 …

Minkowski valuations intertwining with the special linear group Page 1 DOI 10.4171/JEMS/341
J. Eur. Math. Soc. 14, 1565–1597 c European Mathematical Society 2012 Christoph Haberl …

Let $ K $ be a convex body in $\mathbb R^ n $. We introduce a new affine invariant, which
we call $\Omega_K $, that can be found in three different ways: as a limit of normalized …

Little known relations of the renown concept of the halfspace depth for multivariate data with
notions from convex and affine geometry are discussed. Maximum halfspace depth may be …

Abstract Quite recently, an Orlicz Minkowski problem has been posed and the existence part
of this problem for even measures has been presented. In this paper, the existence part of …