Upper estimates on self-perimeters of unit circles for gauges

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

Abstrakty

EN

Let M² denote a Minkowski plane, i.e., an affine plane whose metric is a gauge induced by a compact convex figure B which, as a unit circle of M², is not necessarily centered at the origin. Hence the self-perimeter of B has two values depending on the orientation of measuring it. We prove that this self-perimeter of B is bounded from above by the four-fold self-diameter of B. In addition, we derive a related non-trivial result on Minkowski planes whose unit circles are quadrangles.

Kategorie tematyczne

• 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
• 52A10: Convex sets in 2 dimensions (including convex curves)
• 28A75: Length, area, volume, other geometric measure theory
• 52A38: Length, area, volume
• 46B20: Geometry and structure of normed linear spaces
• 52A40: Inequalities and extremum problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 142
• Numer: 2
• Strony: 179-210

Daty

wydano

2016

Twórcy

autor

Horst Martini

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

autor

Anatoliy Shcherba

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

Identyfikatory

DOI

10.4064/cm142-2-3