Properties of distance functions on convex surfaces and applications

Title:

Properties of distance functions on convex surfaces and applications

Creator:

Rataj, Jan and Zajíček, Luděk

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f3b306f8-4e3f-451c-b324-80390f92defc
uuid:f3b306f8-4e3f-451c-b324-80390f92defc

Subject:

distance function, convex surface, Alexandrov space, DC manifold, ambiguous locus, skeleton, and $r$-boundary

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

If $X$ is a convex surface in a Euclidean space, then the squared intrinsic distance function $\mathop {{\rm dist}}^2(x,y)$ is DC (d.c., delta-convex) on $X\times X$ in the only natural extrinsic sense. An analogous result holds for the squared distance function $\mathop {{\rm dist}}^2(x,F)$ from a closed set $F \subset X$. Applications concerning $r$-boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface are given.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

247-269

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:1

Harvested from:

CDK

Metadata only:

false