8 citations · 13 across the 2 of their papers we have counts for
3 papers
math.DG2013★ 5 cited
Maximization of the first nontrivial eigenvalue on the surface of genus two
Mikhail A. Karpukhin
The first nontrivial eigenvalue of the Laplacian can be considered as a functional on the space of all Riemannian metrics of unit volume on a fixed surface. In this paper we prove…
math.SP2012★ 8 cited
Non-maximality of known extremal metrics on torus and Klein bottle
Mikhail A. Karpukhin
El Soufi-Ilias' theorem establishes a connection between minimal submanifolds of spheres and extremal metrics for eigenvalues of the Laplace-Beltrami operator. Recently, this conne…
math.DG2012
Spectral properties of bipolar surfaces to Otsuki tori
Mikhail A. Karpukhin
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. S…