Event
Mikhail Karpukhin, Caltech, Daniel Stern, University of Chicago
Monday, April 25, 2022 12:00to13:00
GEMSTONE mini-course: Harmonic maps, minimal surfaces, and shape optimization in spectral geometry.
Lecture 1
April 25
Introduction to eigenvalue optimisation problems for surfaces. Hersch's theorem: round metric on the sphere maximizes the first eigenvalue. Li-Yau's conformal volume with an application to the sharp eigenvalue bounds on the projective plane.
Lecture 2April 27Min-max theory for the energy of sphere-value valued maps. Regularity of conformally maximizing metrics.Lecture 3April 29 Stability of maximizing metrics. Applications to the optimization of Steklov eigenvalues on surfaces with many boundary components.
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