On the shape of the moduli of spherical minimal immersions

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)2425-2446
Number of pages22
JournalTransactions of the American Mathematical Society
Volume358
Issue number6
DOIs
StatePublished - Jun 1 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Convex set
  • Distortion
  • Extremal point

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