Minkowski symmetrizations of star shaped sets
نویسندگان
چکیده
منابع مشابه
Note on Star-shaped Sets
1. The aim of this note is to prove that if 717" is a compact subset of En and for some m every w-dimensional hyperplane through a fixed point pQEn intersects M along a nonempty acyclic set, lúm^n — 1, then M is star-shaped with respect to p, i.e., if aQM then the segment pa is contained in M. This theorem is a generalization of a theorem of Aumann [l]. We gave recently a proof of Aumann's theo...
متن کاملRandom symmetrizations of measurable sets
In this paper we prove almost sure convergence to the ball, in the Nikodym metric, of sequences of random Steiner symmetrizations of bounded Caccioppoli and bounded measurable sets, paralleling a result due to Mani-Levitska concerning convex bodies. AMS classification: 60D05, 52A40, 28A05
متن کاملInvariant Valuations on Star-Shaped Sets
The Brunn Minkowski theory of convex bodies and mixed volumes has provided many tools for solving problems involving projections and valuations of compact convex sets in Euclidean space. Among the most beautiful results of twentieth century convexity is Hadwiger's characterization theorem for the elementary mixed volumes (Quermassintegrals); (see [3, 5, 9]). Hadwiger's characterization leads to...
متن کاملModelling and simulating star-shaped random sets
Lévy particles provide a flexible framework for modelling and simulating threedimensional star-shaped random sets. The radial function of a Lévy particle arises from a kernel smoothing of a Lévy basis, and is associated with an isotropic random field on the sphere. If the kernel is proportional to a von Mises–Fisher density, or uniform on a spherical cap, the correlation function of the associa...
متن کاملConvex and star-shaped sets associated with stable distributions
It is known that each symmetric stable distribution in Rd is related to a norm on Rd that makes Rd embeddable in Lp([0, 1]). In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to a convex set in Rd called a zonoid. This work exploits most recent advances in convex geometry in order to come up with new probabilistic results for multivariate stab...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2016
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-016-0159-z