On the shape of the moduli of spherical minimal immersions
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- by Gabor Toth PDF
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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 $\sigma _m$, $m\geq 1$, associated to a compact convex body $\mathcal {L}$ with base point $\mathcal {O}$ in the interior of $\mathcal {L}$. The invariant $\sigma _m$ measures how lopsided $\mathcal {L}$ is in dimension $m$ with respect to $\mathcal {O}$. The results are then appplied to the DoCarmo-Wallach moduli space. We also give an efficient algorithm to calculate $\sigma _m$ for convex polytopes.References
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Additional Information
- Gabor Toth
- Affiliation: Department of Mathematics, Rutgers University, Camden, New Jersey 08102
- Email: gtoth@crab.rutgers.edu
- Received by editor(s): April 7, 2004
- Published electronically: January 24, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 2425-2446
- MSC (2000): Primary 53C42
- DOI: https://doi.org/10.1090/S0002-9947-06-04081-5
- MathSciNet review: 2204039