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.