On the shape of the moduli of spherical minimal immersions

The DoCarmo-Wallach moduli space parametrizing spherical minimal immersions of a Riemannian manifold is a compact convex body in a linear space of tracefree symmetric endomorphisms of an eigenspace of . In this paper we define and study a sequence of metric invariants , , associated to a compact convex body with base point in the interior of . The invariant measures how lopsided is in dimension with respect to . The results are then appplied to the DoCarmo-Wallach moduli space. We also give an efficient algorithm to calculate for convex polytopes.