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.

Posted on Nov 11, 2024 in Differential Equations, Seminars