# [Banach] Abstract of a paper by Konrad J Swanepoel

Dale Alspach alspach at www.math.okstate.edu
Mon Jul 23 07:45:44 CDT 2007

This is an announcement for the paper "Extremal problems in Minkowski
space related to minimal networks" by Konrad J Swanepoel.

Abstract: We solve the following problem of Z. F\"uredi, J. C.
Lagarias and F. Morgan [FLM]: 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 raised in [FLM] that arose out of the study
of singularities in length-minimizing networks in Minkowski spaces.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 52A40 (Primary) 52A21, 49Q10
(Secondary)

Citation: Proceedings of the American Mathematical Society 124
(1996)

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http://front.math.ucdavis.edu/0707.3052

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http://arXiv.org/abs/0707.3052

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