## Extremal problems in Minkowski space related to minimal networks

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- by K. J. Swanepoel
- Proc. Amer. Math. Soc.
**124**(1996), 2513-2518 - DOI: https://doi.org/10.1090/S0002-9939-96-03370-9
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## 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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## Bibliographic 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