Special Session 91: Geometric evolution problems

Analysis of Critical Points of Conformally Invariant Curvature Energies in 4d
Yann Bernard
Monash University
Australia
Co-Author(s):    Tian Lan, Dorian Martino, Tristan Riviere
Abstract:
We consider the Euler--Lagrange equations satisfied by the critical points of a large class of conformally invariant extrinsic energies for 4-manifolds immersed into Euclidean space. Using invariances and Noether`s theorem, we convert the Euler--Lagrange equation into a system of equations with analytically favourable structures, and we develop small-energy estimates. This generalises to the four-dimensional setting ideas originally developed for the Willmore energy in two dimensions.