Approximation of the Euclidean ball by polytopes

Tom 173 / 2006

Monika Ludwig, Carsten Schütt, Elisabeth Werner Studia Mathematica 173 (2006), 1-18 MSC: Primary 52A20. DOI: 10.4064/sm173-1-1

Streszczenie

There is a constant $c$ such that for every $n\in\mathbb N$, there is an $N_{n}$ so that for every $N\geq N_{n}$ there is a polytope $P_{}$ in $\mathbb R^{n}$ with $N$ vertices and $$ \mathop{\rm vol}\nolimits _{n}(B_{2}^{n}\mathbin{\triangle} P) \leq c \mathop{\rm vol}\nolimits _{n}(B_{2}^{n})N^{-\frac{2}{n-1}} $$ where $B_{2}^{n}$ denotes the Euclidean unit ball of dimension $n$.

Autorzy

  • Monika LudwigInstitut für Diskrete Mathematik und Geometrie
    Technische Universität Wien
    Wiedner Hauptstraße 8-10/104
    1040 Wien, Austria
    e-mail
  • Carsten SchüttMathematisches Seminar
    Christian Albrechts Universität
    D-24098 Kiel, Germany
    e-mail
  • Elisabeth WernerDepartment of Mathematics
    Case Western Reserve University
    Cleveland, OH 44106, U.S.A.
    and
    Université de Lille 1
    UFR de Mathématique
    59655 Villeneuve d'Ascq, France
    e-mail

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