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

Abstract

For a compact Riemannian manifold $(M, g_2)$ with constant $Q$-curvature of dimension $n\geq 6$ satisfying nondegeneracy condition, we show that one can construct many examples of constant $Q$-curvature manifolds by gluing construction. We provide a general procedure of gluing together $(M,g_2)$ with any compact manifold $(N, g_1)$ satisfying a geometric assumption. In particular, we can prove that there exists a metric with constant $Q$-curvature on the connected sum $N #M$.