Departamento de Matemáticas UAM

Conformal geometry is the study of invariants which are preserved under ”angle preserving” or ”conformal” maps. In this talk, we will describe some PDE approach to the study of a class of integral conformal invariants. Start with the integral of Gauss curvature on compact surfaces, we will continue on the study of a class of integral conformal invariants on 4-manifolds with applications to the study of topology and diffeomorphism type of the class. I will describe the relevance of a 4-th order linear operator with leading symbol the bi-Laplace operator (part of the family of GJMS operator) in the study of prescribing the Gauss-Bonnet integrand on 4-manifolds under conformal change of metrics. The talk will be expository in nature with self-contained background materials.