Existence of harmonic maps and spectral geometry of Schroedinger operators

Daniel Stern, University of Chicago
Fine Hall 314

’ll discuss recent progress on the existence theory for harmonic maps, in particular the 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’ll see that every manifold carries a canonical family of sphere-valued harmonic maps, which (in dimension<6) stabilize at a solution of a spectral isoperimetric problem generalizing the conformal maximization of  Laplace eigenvalues on surfaces.

Based on joint work with Mikhail Karpukhin.