On the structure of convex sets with applications to the moduli of spherical minimal immersions
In the paper under review, the author studies some properties of certain affine invariant measures of symmetry associated to a compact convex body \(\mathcal{L}\) in \(\mathbb{R}^n\) introduced in his earlier paper [Trans. Am. Math. Soc. 358, No. 6, 2425--2446 (2006; Zbl 1108.53032)]. As functions of the interior of \(\mathcal{L}\), these measures of symmetry are proved or disproved to be concave in some specific situations. Some applications for the DoCarmo-Wallach moduli space of spherical minimal immersions are obtained.
scientific article; zbMATH DE number 5345502