This is an announcement for the paper "Affine invariant points" by Mathieu Meyer, Carsten Schuett, and Elisabeth M. Werner.

Abstract: We answer in the negative a question by Gruenbaum who asked if there exists a finite basis of affine invariant points. We give a positive answer to another question by Gruenbaum 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 n-dimensional Euclidean space, is dense in the set of convex bodies. Crucial to establish these results, are new affine invariant points, not previously considered in the literature.

Archive classification: math.FA

Submitted from: elisabeth.werner@case.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1301.2606

or

http://arXiv.org/abs/1301.2606