New characterization of plurisubharmonic functions and its applications

In this talk, we give a new characterization of plurisubharmonic functions, i.e. an upper semicontinuous function (may take values to be) is plurisubharmonic if it satisfiesmultiple Lp extension property. By using fiber-product powers of holomorphic family as well as tensor product powers of involved line bundle, we can apply this new characterization to get simple proofs of the following important results: plurisubharmonic variation of m-Bergman kernels and positivity of direct image sheaf. This is a joint work with Prof. Fusheng Deng, Liyou Zhang and Xiangyu Zhou.