Extremal spectral properties of Otsuki tori

Abstract

Otsuki tori form a countable family of immersed minimal two-dimensional tori in the unitary three-dimensional sphere. According to El Soufi-Ilias theorem, the metrics on the Otsuki tori are extremal for some unknown eigenvalues of the Laplace-Beltrami operator. Despite the fact that the Otsuki tori are defined in quite an implicit way, we find explicitly the numbers of the corresponding extremal eigenvalues. In particular we provide an extremal metric for the third eigenvalue of the torus.

14 pages, 1 figure. v.2: minor corrections v.3: references are updated. arXiv admin note: text overlap with arXiv:1009.0285

References in corpus (1)

• Laplacian eigenvalues functionals and metric deformations on compact manifolds

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