To the families of geometric measures of convex bodies (the area measures of Aleksandrov‐
Fenchel‐Jessen, the curvature measures of Federer, and the recently discovered dual …

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 …

A new family of geometric Borel measures on the unit sphere is introduced. Special cases
include the L p surface area measures (which extend the classical surface area measure of …

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 …

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 …

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 …

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 …

We consider valuations defined on polytopes containing the origin which have measures on
the sphere as values. We show that the classical surface area measure is essentially the …

This paper aims to develop the basic theory for the dual Orlicz L ϕ affine and geominimal
surface areas of star bodies. Basic properties of these new affine invariants are established …

Abstract The Orlicz–Brunn–Minkowski theory received considerable attention recently, and
many results in the L p-Brunn–Minkowski theory have been extended to their Orlicz …