The -th eigenvalue 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 present paper a new countable family of extremal metrics on the torus is provided.
Cite this article
Mikhail Karpukhin, Spectral properties of bipolar surfaces to Otsuki tori. J. Spectr. Theory 4 (2014), no. 1, pp. 87–111DOI 10.4171/JST/63