Properties of distance functions on convex surfaces and applications

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...

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...

Some Properties of Meromorphic Alpha-convex Functions and Its Applications

The aim of the present paper is to obtain sufficient condition for the class of meromorphic alpha convex functions of order ξ and then to study mapping properties of an integral operator. Many known results apear as special consequences of our work.

On Non-smooth Convex Distance Functions

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points