Connected sum construction of constant Qcurvature manifolds in higher dimensions
Connected sum construction of constant Qcurvature manifolds in higher dimensions

YuehJu Lin , University of Notre Dame
Fine Hall 314
This is a special talk in addition to the 3:00 pm talk on the same date. In geometric analysis, gluing constructions are wellknown methods to create new solutions to nonlinear PDEs from existing ones. For a compact Riemannian manifold (M, g) of dimension n at least 6 with constant Qcurvature and satisfying a nondegeneracy condition, we show that one can construct many other examples of constant Qcurvature manifolds by a gluing construction. In particular, we prove the existence of solutions of a fourthorder PDE, which implies the existence of a smooth metric with constant Qcurvature on the connected sum. In this talk, I will begin with denitions of Qcurvature and some background, and then give an overview of the gluing procedure.