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Proceedings of the American Mathematical Society

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

 

 

Two notes on metric geometry


Author: Ralph Alexander
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
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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 \vert {p - q} \vert 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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DOI: https://doi.org/10.1090/S0002-9939-1977-0442831-5
Keywords: Metric, invariant measure, inversion, Cayley-Menger determinant
Article copyright: © Copyright 1977 American Mathematical Society