Extremal problems in Minkowski space

related to minimal networks

Author:
K. J. Swanepoel

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

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Abstract | References | Similar Articles | Additional Information

Abstract: We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan (1991): Is there an upper-bound polynomial in for the largest cardinality of a set of unit vectors in an -dimensional Minkowski space (or Banach space) such that the sum of any subset has norm less than 1? We prove that and that equality holds iff the space is linearly isometric to , the space with an -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.

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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

DOI:
https://doi.org/10.1090/S0002-9939-96-03370-9

Keywords:
Minimal networks,
Minkowski spaces,
finite-dimensional Banach spaces,
sums of unit vectors problem

Received by editor(s):
February 21, 1995

Communicated by:
Peter Li

Article copyright:
© Copyright 1996
American Mathematical Society