The 2018 Excelsior Lectures

On a fourth-order PDE and applications to problems in conformal geometry

Sun-Yung Alice Chang (Princeton University)

Abstract: In this talk, I will report the study of a 4-th order linear operator P₄ with leading symbol

the bi-Laplace operator discovered by Paneitz in 1983. It turns out P₄ is a special case

of the general class of GJMS operators with ”conformal invariant” properties. I will report

some recent progress on the study of P₄ and its associated curvature Q₄ on general

n-dimensional manifolds with emphasis on the case when n = 4. I will also discuss some

matching 3-rd order boundary operator of P₄ on manifolds with boundary and some geometric

applications.