The DoCarmo-Wallach moduli space parametrizing spherical minimal immersions of a Riemannian manifold M is a compact convex body in a linear space of tracefree symmetric endomorphisms of an eigenspace of M. In this paper we define and study a sequence of metric invariants σ m, m ≥ 1, associated to a compact convex body ℒ with base point O in the interior of ℒ. The invariant σ m measures how lopsided ℒ is in dimension m with respect to O. The results are then appplied to the DoCarmo-Wallach moduli space. We also give an efficient algorithm to calculate σ m for convex polytopes.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Convex set
- Extremal point