Existence of harmonic maps and spectral geometry of Schroedinger operators
Existence of harmonic maps and spectral geometry of Schroedinger operators
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Daniel Stern, University of Chicago
鈥檒l discuss recent progress on the existence theory for harmonic maps, in particular the听existence of harmonic maps of optimal regularity from manifolds of dimension n>2 to every non-aspherical closed manifold containing no stable minimal two-spheres. As an application, we鈥檒l see that every听manifold carries a canonical family of sphere-valued harmonic maps, which (in dimension<6)听stabilize at a solution of a spectral isoperimetric problem generalizing the conformal maximization of听听Laplace eigenvalues on surfaces.
Based on joint work with Mikhail Karpukhin.