Extreme points of the distance function on convex surfaces

Extreme Points of Polar Convex Sets

Properties of Distance Functions on Convex Surfaces and Alexandrov Spaces

If X is a convex surface in a Euclidean space, then the squared (intrinsic) distance function dist(x, y) is d.c. (DC, delta-convex) on X×X in the only natural extrinsic sense. For the proof we use semiconcavity (in an intrinsic sense) of dist(x, y) on X × X if X is an Alexandrov space with nonnegative curvature. Applications concerning r-boundaries (distance spheres) and the ambiguous locus (ex...

Properties of Distance Functions on Convex Surfaces and Applications

If X is a convex surface in a Euclidean space, then the squared intrinsic distance function dist(x, y) is DC (d.c., delta-convex) on X×X in the only natural extrinsic sense. An analogous result holds for the squared distance function dist(x,F ) from a closed set F ⊂ X. Applications concerning r-boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface...

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Extreme Points in Convex Sets of Symmetric Matrices

This paper deals with the following problem: What are the extreme points of a convex set K of n X n matrices, which is the intersection of the set S„ of symmetric matrices of nonnegative type, with another convex subset of symmetric matrices HI In the case where the facial structure of H is known, we expose a general method to determine the extreme points of K (Theorem 1). Then, we apply this m...