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

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10126164" target="_blank" >RIV/00216208:11320/12:10126164 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

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

  • Original language 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^nF. 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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GA201%2F09%2F0067" target="_blank" >GA201/09/0067: Theory of real functions and descriptive set theory II</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2012

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Houston Journal of Mathematics

  • ISSN

    0362-1588

  • e-ISSN

  • Volume of the periodical

    38

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    23

  • Pages from-to

    445-467

  • UT code for WoS article

    000309169800008

  • EID of the result in the Scopus database