PDE Seminar Abstracts

Four-Dimensional Willmore-type Energy and the Bach Equation

Yann Bernard
Monash University, Melbourne, Australia
Fri 13th Jan 2023, 11-12am, Eastern Avenue Seminar Room 403


In this talk, I will introduce new conformally invariant functionals for a four-dimensional hypersurface. I will show how they extend the Willmore 2-dimensional problem and more importantly how they relate to a well-known conformally-invariant *intrinsic* energy whose critical points are known as Bach-flat manifolds. Using techniques inspired and adapted from 2-d, I will prove that Bach-flat immersions that lie in the critical space \(W^{3,2}\cap W^{1,\infty }\) are in fact smooth.