Extremal problems in Minkowski space related to minimal networks
Author:
K. J. Swanepoel
Journal:
Proc. Amer. Math. Soc. 124 (1996), 25132518
MSC (1991):
Primary 52A40, 52A21, 49F10
MathSciNet review:
1327047
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Abstract: We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan (1991): Is there an upperbound 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 lengthminimizing 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:
http://dx.doi.org/10.1090/S0002993996033709
PII:
S 00029939(96)033709
Keywords:
Minimal networks,
Minkowski spaces,
finitedimensional 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
