Geometric PDE Seminar

In this talk, we shall review the convexity of solutions of elliptic partial differential equations; we concentrate on the constant rank theorem for the hessian of the convex solution. As for the interesting from geometry problems, recently we have established some constant rank theorem for the partial convex solutions for some elliptic partial equations. At last we give some geometry applications on the prescribed curvature problems. This is joint work with Fei Han (USTC) and Damin Wu (OSU).