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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On closed curves in Minkowski spaces
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by H. S. Witsenhausen PDF
Proc. Amer. Math. Soc. 35 (1972), 240-241 Request permission

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
  • Hans Herda, Research Problems: A Conjectured Characterization of Circles, Amer. Math. Monthly 78 (1971), no. 8, 888–889. MR 1536460, DOI 10.2307/2316488
    • 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. A. M. Fink, A circle maximizes the minimum pseudo-diameter (written communication). R. Ault, Metric characterization of circles (written communication).
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 240-241
  • MSC: Primary 53C70; Secondary 52A50
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0296880-6
  • MathSciNet review: 0296880