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

For a compact Riemannian manifold $(M, g_2)$ of dimension $ngeq 6$ with constant $Q$-curvature satisfying a nondegeneracy condition, we show that one can construct many other examples of constant $Q$-curvature manifolds by a gluing construction. In this dissertation, we provide a general procedure of gluing together $(M,g_2)$ with any compact manifold $(N, g_1)$ satisfying a natural geometric assumption. In particular, we prove the existence of solutions of a fourth-order partial differential equation, which implies the existence of a smooth metric with constant $Q$-curvature on the connected sum $N#M$.