Abstract
There are two topics in this paper. One is Convex Hull Property of p-harmonic maps, and the other is Liouville theorems on manifolds with weighted poincare' inequality. 1.Convex Hull Property Of P-harmonic Maps： In this paper, we introduce the p-harmonic maps on complete manifolds to Cartan-Hadamard manifolds and estimate the image of the maps. We give the upper bound for the maximum number of disjoint massive sets. 2.Liouville Theorems On Manifolds With Weighted Poincare' Inequality： Let M be a complete noncompact manifold with some Ricci curvature lower bound and N be a complete manifold with nonpositive sectional curvature. We prove the Liouville property on harmonic maps from M to N provided that the weighted Poincare' inequality holds and the Dirichlet energy function of the harmonic map has a proper growth.