Affine invariant points

Mathieu Meyer; Carsten Schütt; Elisabeth M. Werner

doi:10.1007/s11856-015-1196-2

Affine invariant points

Mathieu Meyer, Carsten Schütt, Elisabeth M. Werner

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We answer in the negative a question by Grünbaum who asked if there exists a finite basis of affine invariant points. We give a positive answer to another question by Grünbaum about the “size” of the set of all affine invariant points. Related, we show that the set of all convex bodies K, for which the set of affine invariant points is all of ℝⁿ, is dense in the set of convex bodies. Crucial to establish these results are new affine invariant points, not previously considered in the literature.

Original language	English (US)
Pages (from-to)	163-192
Number of pages	30
Journal	Israel Journal of Mathematics
Volume	208
Issue number	1
DOIs	https://doi.org/10.1007/s11856-015-1196-2
State	Published - Sep 1 2015
Externally published	Yes

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© 2015, Hebrew University of Jerusalem.

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Affine invariant points

Abstract

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