Saikat Mazumdar (McGill University)

Title: Q-curvature, Paneitz operator and a maximum principle
Abstract: In this talk, I will discuss the higher-order version of the Yamabe problem: "Given a compact Riemannian manifold (M,g), does there exist a metric conformal to g with constant Q-curvature"? The behaviour of Q-curvature under conformal changes of the metric is governed by certain conformally covariant powers of the Laplacian. The problem of prescribing the Q-curvature in a conformal class then amounts to solving a nonlinear elliptic PDE involving the powers of Laplacian called the GJMS operator. In general the explicit form of this GJMS operator is not explicitly known. This together with a lack of maximum principle for polyharmonic operators makes the problem challenging. In this talk, I will mainly focus on the biharmonic case and survey some recent developments.