| For a compact Riemannian manifold (M, g2) of dimension n ≥ 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, g2) with any compact manifold ( N, g1) 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... |
