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

• Autorzy: Horst Martini , Anatoly Shcherba
• Języki publikacji: EN

Abstrakty

EN

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 + ε for a sufficiently small ε, then there exists an affinely regular hexagon S such that S ⊂ B ⊂ (1 + 6∛ε) S.

Kategorie tematyczne

• 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
• 52A10: Convex sets in 2 dimensions (including convex curves)
• 52A38: Length, area, volume
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 1
• Strony: 69-87

Daty

wydano

2013

Twórcy

autor

Horst Martini

• Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany

autor

Anatoly Shcherba

• Department of Industrial Computer Technologies, Cherkassy State Technological University, Shevchenko Blvd. 460, Cherkassy 18006, Ukraine

Identyfikatory

DOI

10.4064/cm131-1-7