Simplicial intersections of a convex set and moduli for spherical minimal immersions
نویسندگان
چکیده
منابع مشابه
Moduli for Spherical Eigenmaps and Minimal Immersions
Eigenmaps and spherical minimal immersions of round spheres into round spheres form an interesting subject that has been studied by many authors. The components of an eigenmap are eigenfunctions of the Laplace-Beltrami operator on Sm, the Euclidean m-sphere, m ≥ 2; and the eigenfunctions correspond to a fixed eigenvalue λk, k ≥ 1. Given m ≥ 2 and k ≥ 1, these eigenmaps can be parametrized by a ...
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The DoCarmo-Wallach theory studies isometric minimal immersions f : G/K → S of a compact Riemannian homogeneous space G/K into Euclidean n -spheres for various n . For a given domain G/K , the moduli space of such immersions is a compact convex body in a representation space for the Lie group G . In 1971 DoCarmo and Wallach gave a lower bound for the (dimension of the) moduli for G/K = S , and ...
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We study the properties of certain affine invariant measures of symmetry associated to a compact convex body L in a Euclidean vector space. As functions of the interior of L, these measures of symmetry are proved or disproved to be concave in specific situations, notably for the reduced moduli of spherical minimal immersions. MSC 2000: 53C42
متن کاملSpherical Minimal Immersions of Spherical Space Forms
Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ:M → S(r) ⊂ R is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace operator on M for the same eigenvalue. And conve...
متن کاملMinimal Immersions of Spheres and Moduli
Minimal immersions of round spheres into round spheres, or spherical minimal immersions for short, or “spherical soap bubbles”, belong to a fast growing and fascinating area between algebra and geometry. This theory has rich interconnections with a variety of mathematical disciplines such as invariant theory, convex geometry, harmonic maps, and orthogonal multiplications. In this survey article...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2004
ISSN: 0026-2285
DOI: 10.1307/mmj/1091112079