Geometric Analysis Seminar
Friday, October 9, 2015 - 2:30pm
Malott 206
Paneitz operator is a 4th order operator formed by adding lower order terms to the bi-Laplacian operator on Riemannian manifolds with dimension at least 3. In dimension 4, it behaves analogous to the classical Laplacian operator on surface. In dimension at least 5, together with associated Q curvature it bahaves similar to conformal Laplacian operator and scalar curveture. I will discuss some recent progerss in understanding this operator which overcomes the difficulty of being 4th forder. Among other things, we will discuss infinite series expansion of its Green's function, positive mass theorem and existence of constant Q curvature metrics in a fixed conformal class.