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Alexei V. Penskoi
Researcher at National Research University – Higher School of Economics
Publications - 42
Citations - 309
Alexei V. Penskoi is an academic researcher from National Research University – Higher School of Economics. The author has contributed to research in topics: Eigenvalues and eigenvectors & Isoperimetric inequality. The author has an hindex of 10, co-authored 41 publications receiving 267 citations. Previous affiliations of Alexei V. Penskoi include Moscow State University & Centre de Recherches Mathématiques.
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An isoperimetric inequality for Laplace eigenvalues on the sphere
TL;DR: Nadirashvili and Sire as mentioned in this paper showed that for any positive integer k, the k-th nonzero eigenvalue of the Laplace-Beltrami operator on the two-dimensional sphere endowed with a Riemannian metric of unit area, is maximized in the limit by a sequence of metrics converging to a union of k touching identical round spheres.
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Extremal metrics for eigenvalues of the Laplace-Beltrami operator on surfaces
TL;DR: A survey of recent results in the theory of extremal metrics on surfaces can be found in this article, where a more detailed survey of the recent results is presented in Section 2.1.
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An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane
TL;DR: In this article, the second non-zero eigenvalue of the Laplace-Beltrami operator on the real projective plane was shown to be at most 6.
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Extremal spectral properties of Otsuki tori
TL;DR: In this article, it was shown that the Otsuki tori are extremal for unknown eigenvalues of the Laplace-Beltrami operator for the third eigenvalue of the torus.
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Conformally maximal metrics for Laplace eigenvalues on surfaces
TL;DR: In this paper, it was shown that for a given k, the maximum of the k-th Laplace eigenvalue in a conformal class on a surface is either attained on a metric which is smooth except possibly at a finite number of conical singularities, or it is attained in the limit while a "bubble tree" is formed on the surface.