Rigidity of critical metrics in dimension four

Friday, November 19, 2010 -
4:00pm to 6:00pm
The general quadratic curvature functional is considered in dimension four. It is possible to "gauge" the Euler-Lagrange equations, in a self-adjoint fashion, to become elliptic. Fredholm theory may then be used to describe local properties of the moduli space of critical metrics. I'll show that a number of compact examples are infinitesimally rigid, and are therefore isolated as critical metrics. I'll also discuss solutions of the gauged linearized equation on several noncompact examples which are asymptotically locally Euclidean. This is joint work with Matt Gursky.
Jeff Viaclovsky
University of Wisconsin
Event Location: 
Fine Hall 314