Affine invariant points

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.

• Publication year

  2013

• Venue

  Israel Journal of Mathematics

• Publication date

  2013-01-11

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1007/S11856-015-1196-2arXiv 1301.2606
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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