Abstract
The i-th eigenvalue λi of the Laplace-Beltrami operator on a surface can be considered as a functional on the space of all Riemannian metrics of unit volume on this surface. Surprisingly, only few examples of extremal metrics for these functionals are known. In the first part of the present paper a new countable family of extremal metrics on the torus is provided. In the second part the maximality of all know extremal metrics on torus is investigated. 2010 Mathematics Subject Classification. 58E11, 58J50.
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