Connected sum construction of constant Q-curvature manifolds in higher dimensions

Connected sum construction of constant Q-curvature manifolds in higher dimensions

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Yueh-Ju 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 well-known 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 Q-curvature and satisfying a nondegeneracy condition, we show that one can construct many other examples of constant Q-curvature manifolds by a gluing construction. In particular, we prove the existence of solutions of a fourth-order PDE, which implies the existence of a smooth metric with constant Q-curvature on the connected sum. In this talk, I will begin with denitions of Q-curvature and some background, and then give an overview of the gluing procedure.