Speaker：Rirong Yuan (South China University of Technology)

Time：2023-6-13, 16:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

In this talk we first focus on the structure of nonlinear elliptic equations, going back to the celebrated work of Caffarelli-Nirenberg-Spruck. For a class of fully nonlinear equations, we will determine how close one can come to uniform ellipticity. As applications we will discuss some problem of finding complete conformal metrics with prescribed curvature functions. The assumptions imposed there are almost sharp as shown by a topological obstruction. If time permits, we will talk about the Dirichlet problem for fully nonlinear elliptic equations on Hermitian manifolds.