Abstract
We can extend the Banach-Mazur distance to be a distance between non-symmetric sets by allowing affine transformations instead of linear transformations. It was proved in [J] that for every convex bodyK we haved(K, D)≤n. It is proved that ifK is a convex body in ℝn such thatd(K, D)=n, thenK is a simplex.
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References
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This article is an M.Sc. thesis written under the supervision of E. Gluskin and V.D. Milman at Tel Aviv University.
Partially supported by a G.I.F. grant.
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Palmon, O. The only convex body with extremal distance from the ball is the simplex. Israel J. Math. 80, 337–349 (1992). https://doi.org/10.1007/BF02808075
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DOI: https://doi.org/10.1007/BF02808075