In the Euclidean space E of dimension n; an affine invariant point (resp. set) on the class of convex bodies of dimension $n$, endowed with the Hausdorff metric, is a continuous map from this class into\u00a0 E (resp. into itself ) which is invariant under one-to-one affine transformations\u00a0 of E. Affine invariant points and sets appear to be\u00a0 excellent tools to study the symmetry of a convex body. Answering a number of questions of Grunbaum, we define some new affine points and investigate the notion of dual affine points.<\/p>\n
(joint work with C. Sch\\”utt and E. M. Werner.)<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
In the Euclidean space E of dimension n; an affine invariant point (resp. set) on the class of convex bodies of dimension $n$, endowed with the Hausdorff metric, is a continuous map from this class into\u00a0 E (resp. into itself…
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