A simple geometrie proof of a theorem for starshaped unions of convex sets
A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls
Negative association for a family of random variables means that for any coordinatewise increasing functions f,g we have for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of...
A stability estimate for the Aleksandrow-Fnechel inequality, with an application to mean curvature.
A universal convex set in Euclidean space
A universal convex set in Euclidean space
About a problem of Ulam concerning flat sections of manifolds.
Addition and subtraction of homothety classes of convex sets.
Almost sure asymptotic behaviour of the -neighbourhood surface area of Brownian paths
We show that whenever the -dimensional Minkowski content of a subset exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in , .
An alternative proof of Petty's theorem on equilateral sets
The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth point,...
An analogue of the Krein-Milman theorem for star-shaped sets.
An analytic solution to the Busemann-Petty problem on sections of convex bodies.
An Inequality for the Volume of Inscribed Ellipsoids.
An Optimal Convex Hull Algorithm in Any Fixed Dimension.
Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten.
Approximately generalized convex functions.
Approximation of Convex Bodies by Polytopes with Uniformly Bounded Valences.
Approximation of convex bodies by sums of line segments
Approximation of symmetric convex bodies.
Approximation of the Euclidean ball by polytopes
There is a constant c such that for every n ∈ ℕ, there is an Nₙ so that for every N≥ Nₙ there is a polytope P in ℝⁿ with N vertices and where B₂ⁿ denotes the Euclidean unit ball of dimension n.
Aproximación aleatoria de cuerpos convexos.
Problems related to the random approximation of convex bodies fall into the field of integral geometry and geometric probabilities. The aim of this paper is to give a survey of known results about the stochastic model that has received special attention in the literature and that can be described as follows:Let K be a d-dimensional convex body in Eucliden space Rd, d ≥ 2. Denote by Hn the convex hull of n independent random points X1, ..., Xn distributed identically and uniformly in the interior...