The study of high-dimensional convex bodies from a geometric and analytic point of view,
with an emphasis on the dependence of various parameters on the dimension stands at the …

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 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 …

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 …

We derive a formula connecting the derivatives of parallel section functions of an origin-
symmetric star body in Rn with the Fourier transform of powers of the radial function of the …

The L p dual curvature measure was introduced by Lutwak, Yang & Zhang in an attempt to
unify the L p Brunn–Minkowski theory and the dual Brunn–Minkowski theory. The …

All GL (n) covariant star-body-valued valuations on convex polytopes are completely
classified. It is shown that there is a unique nontrivial such valuation. This valuation turns out …

Abstract The Minkowski problem in Gaussian probability space is studied in this paper. In
addition to providing an existence result on a Gaussian-volume-normalized version of this …

Motivated by basic questions in Minkowski geometry, H. Busemann and CM Petty posed ten
problems about convex bodies in 1956 (see [BP]). The first problem, now known as the …

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 …