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RADO Lecture -- Level surfaces of eigenfunctions

David Jerison
November 30, 2022
4:15 pm - 5:15 pm
Hitchcock Hall 035

Title:  Lecture 1: Level surfaces of eigenfunctions

Speaker:  David Jerison (MIT)

Abstract:  The HOT Spots Conjecture of J. Rauch is an essential test of our understanding of the shapes of level sets of the simplest eigenfunctions. We will describe this question and relate it to other conjectures about level sets. A new variational principle for level sets of eigenfunctions reveals an analogy with mean curvature flow. This suggests that one can hope to apply methods of differential geometry to level sets, in analogy with differential Harnack inequalities in work by R. Hamilton on mean curvature flow and Ricci flow.

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