New Lp affine isoperimetric inequalities Page 1 Advances in Mathematics 218 (2008) 762–780
www.elsevier.com/locate/aim New Lp affine isoperimetric inequalities Elisabeth Wernera,b,∗,1 …

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 We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric
inequalities for mixed p-affine surface areas. We introduce a new class of bodies, the …

Let K be a convex body in ℝn with centroid at 0 and B be the Euclidean unit ball in ℝn
centered at 0. We show that t→0lim\left|K\right|-\left|K_t\right|\left|B\right …

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 …

This paper deals with L p geominimal surface area and its extension to L p mixed
geominimal surface area. We give an integral formula of L p geominimal surface area by the …

This article is dedicated to the Orlicz-Petty bodies. We first propose the homogeneous Orlicz
affine and geominimal surface areas and establish their basic properties such as …

We present a new approach for constructing polytope Lyapunov functions for continuous-
time linear switching systems (LSS). This allows us to decide the stability of LSS and to …