منابع مشابه
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...
متن کاملOn the Cut Locus in Alexandrov Spaces and Applications to Convex Surfaces
Alexandrov spaces are a large class of metric spaces that includes Hilbert spaces, Riemannian manifolds and convex surfaces. In the framework of Alexandrov spaces, we examine the ambiguous locus of analysis and the cut locus of differential geometry, proving a general bisecting property, showing how small the ambiguous locus must be, and proving that typically the ambiguous locus and a fortiori...
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In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...
متن کاملProperties 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...
متن کاملCut Loci and Distance Spheres on Alexandrov Surfaces
The purpose of the present paper is to investigate the structure of distance spheres and cut locus C(K) to a compact set K of a complete Alexandrov surface X with curvature bounded below. The structure of distance spheres around K is almost the same as that of the smooth case. However C(K) carries different structure from the smooth case. As is seen in examples of Alexandrov surfaces, it is pro...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1999
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-99-02193-5