Seminar: On Yamabe-type problems on manifolds with boundary

Seminar| Institute of Mathematical Sciences

Abstract: In this talk, I will present some recent results on the existence and compactness of solutions to Yamabe-type equations on manifolds with boundary. The Yamabe problem plays an important role in the study of conformal geometry and partial differential equations. Geometrically, it establishes conformal metrics on Riemannian manifolds with prescribed curvatures. From a PDE point of view, it corresponds to differential equations with critical nonlinearities. I will discuss recent developments in the field as well as some possible projects of personal interest. The talk is based on joint works with Sergio Almaraz, Chenkai Liu, Olivaine Queiroz and Jerome Vetois.