Abstract: In this talk, we examine a concentration phenomenon for solutions to the constant Q-curvature equation, a critical fourth-order equation on a closed Riemannian manifold. The challenge of finding constant Q-curvature metrics is closely linked to the Yamabe problem and arises from the goal of identifying optimal metrics for a given compact, boundaryless manifold.
In this work, we address the problem on a product Riemannian manifold. We will start by briefly introducing the concept of Q-curvature and then outline the main ideas for finding solutions that concentrate around specific points on the manifold, which are of particular geometric significance.