Critical metrics on connected sums of Einstein fourmanifolds
Critical metrics on connected sums of Einstein fourmanifolds

Jeff Viaclovsky, University of Wisconsin, Madison
Fine Hall 110
THIS IS A JOINT SEMINAR WITH DIFFERENTIAL GEOMETRY & GEOMETRIC ANALYSIS and JOINT PRINCETONRUTGERS GEOMETRIC PDEs. PLEASE NOTE DIFFERENT LOCATION. I will discuss a gluing procedure designed to obtain canonical metrics on connected sums of Einstein fourmanifolds. The main application is an existence result, using two wellknown Einstein manifolds as building blocks: the FubiniStudy metric on CP^2, and the product metric on S^2 x S^2. Using these metrics in various gluing configurations, critical metrics are found on connected sums for a specific Riemannian functional, which depends on the global geometry of the factors. This is joint work with Matt Gursky.