DIFFERENTIAL GEOMETRY AND GEOMETRIC ANALYSIS SEMINAR

4/27/2012

Niels Martin Møller
MIT

Gluing for Nonlinear PDEs, and Self-Shrinking Solitons in Mean Curvature Flow

I will discuss some recent gluing constructions from minimal surface theory that yield complete, embedded, self-shrinking soliton surfaces of large genus g in R^3 (as expected from numerics by Tom Ilmanen and others in the early 90's), by fusing known low-genus examples. The analysis in the case of non-compact ends (joint w/ N. Kapouleas & S. Kleene), is complicated by the unbounded geometry, where Schrödinger operators (of Ornstein-Uhlenbeck type) with fast growth of the coefficients need to be understood well via Liouville-type results, which in turn enable construction of the resolvent of the stability operator and closing the PDE system.