Abstract：Subsolutions play very important roles in the study of fully nonlinear equations. In this talk we shall discuss different notions of subsections and how they can be used in deriving priori estimates for equations on closed manifolds. We shall also show the equivalence between some of the definitions for Type I cones (defined by Caffarelli, Nirenberg and Spruck). In the second part of the talk we shall discuss some preliminary results on gradient estimates for equations on Riemannian manifolds.
