学术报告（周恒宇 6.14）

In this talk we discuss some recent results on the Dirichlet problem of prescribed mean curvature equations in Riemannian manifolds. Our motivations come from the Plateau problem of prescribed mean curvature equations and the construction of Jang graphs in the Shoen-Yau's proof on the positive mass theorem. We relate the solvability of these Dirichlet problems with a toplogical condition (NCf-condition) from the prescribed mean curvature functions. A key ingredient of our proof is a curvature estimate of (Lambda,r)-perimeter minimizer from Simon's idea. An application into the area minimizing problem is also presented.