科研之友
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摘要
We prove sharp inequalities for the average number of affine diameters through the points of a convex body K in R-n. These inequalities hold if K is a polytope or of dimension two. An example shows that the proof given in the latter case does not extend to higher dimensions. The example also demonstrates that for n >= 3 there exist norms and convex bodies K subset of R-n such that the metric projection on K with respect to the metric defined by the given norm is well defined but not a Lipschitz map, which is in striking contrast to the planar or the Euclidean case.
- 出版日期2016-2
