Constant Q-curvature metrics

Início: 20/10/2023 17:00

Término: 20/10/2023 18:00

Palestrante: Rayssa Caju (Universidad de Chile)

E-mail do Palestrante: rayssacaju@gmail.com

Resumo: Over the past few decades, there has been significant exploration of the interplay between geometry and partial differential equations. In particular, some problems arising in conformal geometry, such as the classical Yamabe problem, can be reduced to the study of PDEs with critical exponent on manifolds. More recently, the so-called Q-curvature equation, a fourth-order elliptic PDE with critical exponent, is another class of conformal equations that has drawn considerable attention by its relation with a natural concept of curvature. In this talk, I would like to motivate these problems from a geometric and analytic perspective, and discuss some recent developments in the area, in particular regarding the singular Q-curvature problem.