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.
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- Zokhrab Mustafaev
- Affiliation: Department of Mathematics and Computer Science, 1212 Williams Hall, Ithaca College, Ithaca, New York 14850
- Email: email@example.com
- Received by editor(s): October 28, 2003
- Received by editor(s) in revised form: December 15, 2003
- Published electronically: September 16, 2004
- Communicated by: Jon G. Wolfson
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1231-1237
- MSC (2000): Primary 52A10, 52A40
- DOI: https://doi.org/10.1090/S0002-9939-04-07662-2
- MathSciNet review: 2117226