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Proceedings of the American Mathematical Society

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On closed curves in Minkowski spaces


Author: H. S. Witsenhausen
Journal: Proc. Amer. Math. Soc. 35 (1972), 240-241
MSC: Primary 53C70; Secondary 52A50
MathSciNet review: 0296880
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Abstract: The minimum pseudo-diameter d and the length L of a simple closed rectifiable curve in Minkowski space satisfy $ L \geqq gd$ where g is the half-girth of the unit ball. The bound is sharp.


References [Enhancements On Off] (What's this?)

  • [1] Hans Herda, Research Problems: A Conjectured Characterization of Circles, Amer. Math. Monthly 78 (1971), no. 8, 888–889. MR 1536460, 10.2307/2316488
  • [2] J. J. Schäffer, Inner diameter, perimeter, and girth of spheres, Math. Ann. 173 (1967), 59-79; addendum, ibid. 173 (1967), 79-82. MR 36 #1959.
  • [3] A. M. Fink, A circle maximizes the minimum pseudo-diameter (written communication).
  • [4] R. Ault, Metric characterization of circles (written communication).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296880-6
Keywords: Minkowski spaces, pseudo-diameters, girth of balls
Article copyright: © Copyright 1972 American Mathematical Society