Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the shape of the moduli of spherical minimal immersions


Author: Gabor Toth
Journal: Trans. Amer. Math. Soc. 358 (2006), 2425-2446
MSC (2000): Primary 53C42
Published electronically: January 24, 2006
MathSciNet review: 2204039
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C42

Retrieve articles in all journals with MSC (2000): 53C42


Additional Information

Gabor Toth
Affiliation: Department of Mathematics, Rutgers University, Camden, New Jersey 08102
Email: gtoth@crab.rutgers.edu

DOI: https://doi.org/10.1090/S0002-9947-06-04081-5
Keywords: Convex set, extremal point, distortion
Received by editor(s): April 7, 2004
Published electronically: January 24, 2006
Article copyright: © Copyright 2006 American Mathematical Society