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New affine measures of symmetry for convex bodies

2011; Elsevier BV; Volume: 228; Issue: 5 Linguagem: Inglês

10.1016/j.aim.2011.08.002

1090-2082

Mathieu Meyer, Carsten Schütt, Elisabeth M. Werner,

Prion Diseases and Protein Misfolding

Grünbaum introduced measures of symmetry for convex bodies that measure how far a given convex body is from a centrally symmetric one. Here, we introduce new measures of symmetry that measure how far a given convex body is from one with "enough symmetries". To define these new measures of symmetry, we use affine covariant points. We give examples of convex bodies whose affine covariant points are "far apart". In particular, we give an example of a convex body whose centroid and Santaló point are "far apart".