Measure of Planes Intersecting a Convex Body

Width of convex bodies in spaces of constant curvature

We consider the measure of points, the measure of lines and the measure of planes intersecting a given convex body K in a space form. We obtain some integral formulas involving the width of K and the curvature of its boundary ∂K . Also we study the special case of constant width. Moreover we obtain a generalisation of the Heintze–Karcher inequality to space forms.

Grey Scale Convex Hulls: Definition, Implementation and Application

The convex hull of a set is the smallest convex set containing this set. An equivalent definition consists in intersecting all half-planes containing the set. We show that this latter definition is nothing but an algebraic closing that can be applied to grey scale images. An implementation of this definition leading to a decreasing family of convex hulls with increasing precision is proposed. F...

Some Properties of a Function Originating from Geometric Probability for Pairs of Hyperplanes Intersecting with a Convex Body

In the paper, the authors derive an integral representation, present a double inequality, supply an asymptotic formula, find an inequality, and verify complete monotonicity of a function involving the gamma function and originating from geometric probability for pairs of hyperplanes intersecting with a convex body.

University of Alberta Some Inequalities in Convex Geometry

We present some inequalities in convex geometry falling under the broad theme of quantifying complexity, or deviation from particularly pleasant geometric conditions: we give an upper bound for the Banach–Mazur distance between an origin-symmetric convex body and the n-dimensional cube which improves known bounds when n ≥ 3 and is “small”; we give the best known upper and lower bounds (for high...

Non convex technologies and economic efficiency measure with imprecise data