About: CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Let F be a closed subset of R^n and n = 2 or n = 3. S. Ferry (1975) proved that then, for almost all r > 0, the level set (distance sphere, r-boundary) S^r(F) := {x is an element of R^n : dist(x, F) = r} is a topological (n - 1)-dimensional manifold. This result was improved by J.H.G. Fu (1985). We show that Ferry's result is an easy consequence of the only fact that the distance function d(x) = dist(x, F) is locally DC and has no stationary point in R^n\F. Using this observation, we show that Ferry's (and even Fu's) result extends to sufficiently smooth normed linear spaces X with dim X is an element of {2, 3} (e.g., to l(n)(p), n = 2, 3, p }= 2), which improves and generalizes a result of R. Gariepy and W.D. Pepe (1972). By the same method we also generalize Fu's result to Riemannian manifolds and improve a result of K. Shiohama and M. Tanaka (1996) on distance spheres in Alexandrov spaces. Let F be a closed subset of R^n and n = 2 or n = 3. S. Ferry (1975) proved that then, for almost all r > 0, the level set (distance sphere, r-boundary) S^r(F) := {x is an element of R^n : dist(x, F) = r} is a topological (n - 1)-dimensional manifold. This result was improved by J.H.G. Fu (1985). We show that Ferry's result is an easy consequence of the only fact that the distance function d(x) = dist(x, F) is locally DC and has no stationary point in R^n\F. Using this observation, we show that Ferry's (and even Fu's) result extends to sufficiently smooth normed linear spaces X with dim X is an element of {2, 3} (e.g., to l(n)(p), n = 2, 3, p }= 2), which improves and generalizes a result of R. Gariepy and W.D. Pepe (1972). By the same method we also generalize Fu's result to Riemannian manifolds and improve a result of K. Shiohama and M. Tanaka (1996) on distance spheres in Alexandrov spaces. (en)
Title	CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE (en)
skos:prefLabel	CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE (en)
skos:notation	RIV/00216208:11320/12:10126164!RIV13-GA0-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/09/0067), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Zajíček, Luděk Rataj, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	129060
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10126164
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	positive reach; DC manifold; Alexandrov space; Riemannian manifold; Minkowski space; finite dimensional Banach space; distance sphere; critical point; Distance function (en)
http://linked.open.../riv/klicoveSlovo	Riemannian manifold Distance function distance sphere finite dimensional Banach space positive reach Minkowski space critical point Alexandrov space DC manifold
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[99EC626F0034]
http://linked.open...i/riv/nazevZdroje	Houston Journal of Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Theory of real functions and descriptive set theory II
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	38
http://linked.open...iv/tvurceVysledku	Zajíček, Luděk Rataj, Jan
http://linked.open...ain/vavai/riv/wos	000309169800008
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0362-1588
number of pages	23 (xsd:int)
http://localhost/t...ganizacniJednotka	11320

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 48 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software