摘要：

This talk has two fold. In the first part,  I will discuss some results regarding gradient estimates for positive solutions of nonlinear elliptic equations under geometric flows. As a consequence, some Liouville results are introduced. In the second part, I will show a Liouville theorem for weighted p-Laplacian using nonlinear potential theory and a Liouville result for weighted p-harmonic forms under new curvature conditions in Bochner techniques given by Petersen and Wink.