On the singular Q-curvature problem.

Abstract. The connections between geometry and partial differential equations have been extensively studied in the last decades. 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 discuss how fixed point methods can be helpful to study the Q-curvature equation in a singular setting, and discuss some interesting problems related to this topic. Joint work with J.H. Andrade, J. M do O, J. Ratzkin and A. Silva Santos.

Posted on Oct 5, 2021 in Differential Equations, Seminars