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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Two notes on metric geometry
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by Ralph Alexander PDF
Proc. Amer. Math. Soc. 64 (1977), 317-320 Request permission

Abstract:

If $\mu ,\smallint d\mu = 1$, is a signed Borel measure on the unit ball in ${E^3}$, it is shown that ${\sup _\mu }\smallint \smallint | {p - q} |d\mu (p)d\mu (q) = 2$ with no extremal measure existing. Also, a class of simplices which generalizes the notion of acute triangle is studied. The results are applied to prove inequalities for determinants of the Cayley-Menger type.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 317-320
  • MSC: Primary 52A50
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0442831-5
  • MathSciNet review: 0442831