Event

Alexei Penskoi (Moscow State University and Higher School of Economics)

Monday, August 28, 2017 13:30to14:30
Room 5183, University de Montreal, CA

Abstract: The first subject of this talk is an isoperimetric inequality for the second non-zero eigenvalue of the Laplace-Beltrami operator on the real projective plane (based on a joint paper with N. Nadirashvili). For a metric of area 1 this eigenvalue is not greater than 20\pi. This value could be attained as a limit on a sequence of metrics of area 1 on the projective plane converging to a singular metric on the projective plane and the sphere with standard metrics touching in a point such that the ratio of the areas of the projective plane and the sphere is 3:2. The second subject of this talk is a very recent result (joint paper with M. Karpukhin, N. Nadirashvili and I. Polterovich) about an isoperimetric inequality for Laplace eigenvalues on the sphere. For a metric of area 1 the k-th eigenvalue is not greater than 8\pi k. This value could be attained as a limit on a sequence of metrics of area 1 on the sphere converging to a singular metric on k spheres with standard metrics of equal radius touching in a point.

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