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Two new approaches are presented to establish the existence of polytopal solutions to the
discrete-data Lp Minkowski problem for all p> 1. As observed by Schneider [23], the Brunn …

It is shown that the classical John ellipsoid, the Petty ellipsoid and a recently discovered
'dual'of the Legendre ellipsoid are all special cases (ellipsoids which can be associated with …

Surface bodies and p-affine surface area Page 1 http://www.elsevier.com/locate/aim Advances
in Mathematics 187 (2004) 98–145 Surface bodies and p-affine surface area Carsten …

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 …

VOLUME INEQUALITIES FOR SUBSPACES OF Lp Erwin Lutwak, Deane Yang & Gaoyong
Zhang Abstract Affine isoperimetric inequalities Page 1 j. differential geometry 68 (2004) 159-184 …

Lp Minkowski problem with not necessarily positive data Page 1 Advances in Mathematics 201
(2006) 77–89 www.elsevier.com/locate/aim Lp Minkowski problem with not necessarily positive …

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 …

Assume K⊂ Rd is a convex body and Xn⊂ K is a random sample of n uniform, independent
points from K. The convex hull of Xn is a convex polytope Kn called random polytope …

Stochastic geometry studies randomly generated geometric objects. The present chapter
deals with some discrete aspects of stochastic geometry. We describe work that has been …