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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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Extremal problems in Minkowski space related to minimal networks
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by K. J. Swanepoel PDF
Proc. Amer. Math. Soc. 124 (1996), 2513-2518 Request permission

Abstract:

We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan (1991): Is there an upper-bound polynomial in $n$ for the largest cardinality of a set $S$ of unit vectors in an $n$-dimensional Minkowski space (or Banach space) such that the sum of any subset has norm less than 1? We prove that $|S|\leq 2n$ and that equality holds iff the space is linearly isometric to $\ell ^{n}_{\infty }$, the space with an $n$-cube as unit ball. We also remark on similar questions they raised that arose out of the study of singularities in length-minimizing networks in Minkowski spaces.
References
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Additional Information
  • K. J. Swanepoel
  • Affiliation: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
  • Email: konrad@friedrichs.up.ac.za
  • Received by editor(s): February 21, 1995
  • Communicated by: Peter Li
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 2513-2518
  • MSC (1991): Primary 52A40, 52A21, 49F10
  • DOI: https://doi.org/10.1090/S0002-9939-96-03370-9
  • MathSciNet review: 1327047