Universal constraints on the range of eigenmaps and spherical minimal immersions

Toth, Gabor

doi:10.1090/S0002-9947-99-02252-7

Universal constraints on the range of eigenmaps and spherical minimal immersions
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by Gabor Toth

Trans. Amer. Math. Soc. 351 (1999), 1423-1443

DOI: https://doi.org/10.1090/S0002-9947-99-02252-7

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Abstract:

The purpose of this paper is to give lower estimates on the range dimension of spherical minimal immersions in various settings. The estimates are obtained by showing that infinitesimal isometric deformations (with respect to a compact Lie group acting transitively on the domain) of spherical minimal immersions give rise to a contraction on the moduli space of the immersions and a suitable power of the contraction brings all boundary points into the interior of the moduli space.

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