Metric inequalities and the zonoid problem
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- by H. S. Witsenhausen PDF
- Proc. Amer. Math. Soc. 40 (1973), 517-520 Request permission
Abstract:
For normed spaces the hypermetric and quasihypermetric properties are equivalent and imply the quadrilateral property. The unit ball of a Minkowski space is a zonoid if and only if the dual space is hypermetric. The unit ball of $l_p^n$ is not a zonoid for $n = 3,p < \log 3/\log 2$, and for $p \leqq 2 - {(2n\log 2)^{ - 1}} + o({n^{ - 1}})$. The elliptic spaces ${\mathcal {E}^d},d > 1$, are not quasihypermetric.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 517-520
- MSC: Primary 52A40
- DOI: https://doi.org/10.1090/S0002-9939-1973-0390916-0
- MathSciNet review: 0390916