Affine invariant points

Mathieu Meyer, Carsten Schütt, Elisabeth M. Werner

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 languageEnglish (US)
Pages (from-to)163-192
Number of pages30
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Sep 1 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015, Hebrew University of Jerusalem.


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