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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