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Mathematical Physics Seminar

Thursday, November 21, 2019
3:00pm to 4:00pm
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Linde Hall 289
Isoperimetric inequalities for Laplacian eigenvalues: recent advances
Mikhail Karpukhin, Department of Mathematics, UC Irvine,

The Laplacian is a canonical second order elliptic operator defined on any Riemannian manifold. The study of upper bounds for its eigenvalues is a classical subject of spectral geometry going back to J. Hersch, P. Li and S.-T. Yau. It turns out that the optimal isoperimetric inequalities for Laplacian eigenvalues are closely related to minimal surfaces in spheres, a classical object of geometric analysis. Recently, this connection was used to obtain a variety of new exciting results. In the present talk we will survey some recent advances in the field, including the optimal isoperimetric inequality for all Laplacian eigenvalues on the sphere and the projective plane. The talk is based on joint works with N. Nadirashvili, A. Penskoi and I. Polterovich.

For more information, please contact Math Department by phone at 626-395-4335 or by email at