Geodesic
Properties of distance functions on convex surfaces and applications
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 247-269.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

If X is a convex surface in a Euclidean space, then the squared intrinsic distance function dist2⁡(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 dist2⁡(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 are given.
DOI : 10.1007/s10587-011-0010-5
Classification : 52A20, 53C45
Mots-clés : distance function; convex surface; Alexandrov space; DC manifold; ambiguous locus; skeleton; r-boundary 
@article{10_1007_s10587_011_0010_5,
     author = {Rataj, Jan and Zaj{\'\i}\v{c}ek, Lud\v{e}k},
     title = {Properties of distance functions on convex surfaces and applications},
     journal = {Czechoslovak Mathematical Journal},
     pages = {247--269},
     publisher = {mathdoc},
     volume = {61},
     number = {1},
     year = {2011},
     doi = {10.1007/s10587-011-0010-5},
     mrnumber = {2782772},
     zbl = {1224.53105},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0010-5/}
}
TY  - JOUR
AU  - Rataj, Jan
AU  - Zajíček, Luděk
TI  - Properties of distance functions on convex surfaces and applications
JO  - Czechoslovak Mathematical Journal
PY  - 2011
SP  - 247
EP  - 269
VL  - 61
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0010-5/
DO  - 10.1007/s10587-011-0010-5
LA  - en
ID  - 10_1007_s10587_011_0010_5
ER  - 
%0 Journal Article
%A Rataj, Jan
%A Zajíček, Luděk
%T Properties of distance functions on convex surfaces and applications
%J Czechoslovak Mathematical Journal
%D 2011
%P 247-269
%V 61
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0010-5/
%R 10.1007/s10587-011-0010-5
%G en
%F 10_1007_s10587_011_0010_5
Rataj, Jan; Zajíček, Luděk. Properties of distance functions on convex surfaces and applications. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 247-269. doi : 10.1007/s10587-011-0010-5. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0010-5/
  • Rataj, Jan; Zajíček, Luděk Smallness of the set of critical values of distance functions in two-dimensional Euclidean and Riemannian spaces, Mathematika, Volume 66 (2020) no. 2, pp. 297-324 | DOI:10.1112/mtk.12020 | Zbl:1441.53029

Cité par 1 document. Sources : zbMATH