This HTML5 document contains 49 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
n19http://linked.opendata.cz/resource/domain/vavai/vysledek/RIV%2F00216208%3A11320%2F12%3A10126164%21RIV13-GA0-11320___/
n9http://localhost/temp/predkladatel/
n16http://linked.opendata.cz/resource/domain/vavai/projekt/
n4http://linked.opendata.cz/resource/domain/vavai/riv/tvurce/
n6http://linked.opendata.cz/resource/domain/vavai/subjekt/
n5http://linked.opendata.cz/ontology/domain/vavai/
n11http://linked.opendata.cz/resource/domain/vavai/zamer/
shttp://schema.org/
skoshttp://www.w3.org/2004/02/skos/core#
n3http://linked.opendata.cz/ontology/domain/vavai/riv/
n2http://linked.opendata.cz/resource/domain/vavai/vysledek/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
n7http://linked.opendata.cz/ontology/domain/vavai/riv/klicoveSlovo/
n20http://linked.opendata.cz/ontology/domain/vavai/riv/duvernostUdaju/
xsdhhttp://www.w3.org/2001/XMLSchema#
n18http://linked.opendata.cz/ontology/domain/vavai/riv/aktivita/
n12http://linked.opendata.cz/ontology/domain/vavai/riv/jazykVysledku/
n15http://linked.opendata.cz/ontology/domain/vavai/riv/obor/
n14http://linked.opendata.cz/ontology/domain/vavai/riv/druhVysledku/
n8http://reference.data.gov.uk/id/gregorian-year/

Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10126164%21RIV13-GA0-11320___
rdf:type
n5:Vysledek skos:Concept
dcterms: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.
dcterms: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
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
skos:notation
RIV/00216208:11320/12:10126164!RIV13-GA0-11320___
n5:predkladatel
n6:orjk%3A11320
n3:aktivita
n18:P n18:Z
n3:aktivity
P(GA201/09/0067), Z(MSM0021620839)
n3:cisloPeriodika
2
n3:dodaniDat
n8:2013
n3:domaciTvurceVysledku
n4:7357362 n4:2689928
n3:druhVysledku
n14:J
n3:duvernostUdaju
n20:S
n3:entitaPredkladatele
n19:predkladatel
n3:idSjednocenehoVysledku
129060
n3:idVysledku
RIV/00216208:11320/12:10126164
n3:jazykVysledku
n12:eng
n3:klicovaSlova
positive reach; DC manifold; Alexandrov space; Riemannian manifold; Minkowski space; finite dimensional Banach space; distance sphere; critical point; Distance function
n3:klicoveSlovo
n7:Alexandrov%20space n7:critical%20point n7:distance%20sphere n7:DC%20manifold n7:Minkowski%20space n7:finite%20dimensional%20Banach%20space n7:Distance%20function n7:positive%20reach n7:Riemannian%20manifold
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[99EC626F0034]
n3:nazevZdroje
Houston Journal of Mathematics
n3:obor
n15:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n16:GA201%2F09%2F0067
n3:rokUplatneniVysledku
n8:2012
n3:svazekPeriodika
38
n3:tvurceVysledku
Rataj, Jan Zajíček, Luděk
n3:wos
000309169800008
n3:zamer
n11:MSM0021620839
s:issn
0362-1588
s:numberOfPages
23
n9:organizacniJednotka
11320