On the stability of the unit circle with minimal self-perimeter in normed planes

Tom 131 / 2013

Horst Martini, Anatoly Shcherba Colloquium Mathematicum 131 (2013), 69-87 MSC: 46B20, 52A10, 52A21, 52A38. DOI: 10.4064/cm131-1-7

Streszczenie

We prove a stability result on the minimal self-perimeter $L(B)$ of the unit disk $B$ of a normed plane: if $L(B) = 6 + \varepsilon $ for a sufficiently small $\varepsilon $, then there exists an affinely regular hexagon $S$ such that $S \subset B \subset (1 + 6 \sqrt [3]{\varepsilon }) S$.

Autorzy

  • Horst MartiniFaculty of Mathematics
    University of Technology
    09107 Chemnitz, Germany
    e-mail
  • Anatoly ShcherbaDepartment of Industrial Computer Technologies
    Cherkassy State Technological University
    Shevchenko Blvd. 460
    Cherkassy 18006, Ukraine
    e-mail

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