Geodesic
On the stability of the unit circle with minimal self-perimeter in normed planes
Horst Martini 1   ; Anatoly Shcherba 2
1 Faculty of Mathematics University of Technology 09107 Chemnitz, Germany
2 Department of Industrial Computer Technologies Cherkassy State Technological University Shevchenko Blvd. 460 Cherkassy 18006, Ukraine
Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 69-87 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $S \subset B \subset (1 + 6 \sqrt [3]{\varepsilon }) S$.
DOI : 10.4064/cm131-1-7
Keywords: prove stability result minimal self perimeter unit disk normed plane varepsilon sufficiently small varepsilon there exists affinely regular hexagon subset subset sqrt varepsilon

Horst Martini  1   ; Anatoly Shcherba  2

1 Faculty of Mathematics University of Technology 09107 Chemnitz, Germany
2 Department of Industrial Computer Technologies Cherkassy State Technological University Shevchenko Blvd. 460 Cherkassy 18006, Ukraine 
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Horst Martini; Anatoly Shcherba. On the stability of the unit circle with minimal self-perimeter in normed planes. Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 69-87. doi: 10.4064/cm131-1-7

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