Langue :
Fanny Bastien (Réalisation), Hugo BÉCHET (Réalisation), Daniel Stern (Intervenant)
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Citer cette ressource :
Daniel Stern. I_Fourier. (2021, 1 juillet). D. Stern - Harmonic map methods in spectral geometry , in 2021. [Vidéo]. Canal-U. (Consultée le 11 décembre 2023)

D. Stern - Harmonic map methods in spectral geometry

Réalisation : 1 juillet 2021 - Mise en ligne : 1 juillet 2021
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Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to connections to the study of sphere-valued harmonic maps and minimal immersions. In this talk, I'll describe a series of results which shed new light on this problem by relating it to the variational theory of the Dirichlet energy on sphere-valued maps. Recent applications include new (H^{-1}-)stability results for the maximization of the first and second Laplacian eigenvalues, and a proof that metrics maximizing the first Steklov eigenvalue on a surface of genus g and k boundary components limit to the \lambda_1-maximizing metric on the closed surface of genus g as k becomes large (in particular, the associated free boundary minimal surfaces in B^{N+1} converge as varifolds to the associated closed minimal surface in S^N). Based on joint works with Mikhail Karpukhin, Mickael Nahon and Iosif Polterovich.


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