Title

The ratio of the length of the unit circle to the area of the unit disc in Minkowski planes

Document Type

Article

Publication Date

4-1-2005

Abstract

In their paper "An Introduction to Finsler Geometry," J. C. Alvarez and C. Duran asked if there are other Minkowski planes besides the Euclidean for which the ratio of the Minkowski length of the unit "circle" to the Holmes-Thompson area of the unit disc equals 2. In this paper we show that this ratio is greater than 2, and that the ratio 2 is achieved only for Minkowski planes that are affine equivalent to the Euclidean plane. In other words, the ratio is 2 only when the unit "circle" is an ellipse. © 2004 American Mathematical Society.

Publication Name

Proceedings of the American Mathematical Society

Volume Number

133

First Page

1231

Last Page

1237

Issue Number

4

DOI

10.1090/S0002-9939-04-07662-2

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