The Liouville Property And The Energy Growth Property Of F-Harmonic Maps

In this paper,we mainly study the Bochner-typed formula and Reilly-typed formula of F-harmonic maps and their applications.At last,we also study F-energy growth property,then obtain some results.In chapter 1,we will make a general description on the researches in our field and show the main results of this paper.In chapter 2,we introduce the preliminaries for the paper.In chapter 3,we establish a Bochner-typed formula of F-harmonic maps,and use it to study the Liouville property of F-harmonic maps from the Riemann manifolds which is compact without boundary and has nonnegative Ricci curvature to the Riemann manifolds which has nonpositive sectional curvature.In chapter 4,we establish the Reilly-typed formula of F-harmonic maps and use it to study the Liouville property of a wide class of F-harmonic maps from the Riemann manifolds which is compact and has nonnegative Ricci curvature(including the manifolds with boundary)to the Riemann manifolds which has nonpositive sectional curvature.This case includes the result of chapter 3,but the proof is different.In chapter 5,we discuss the F-energy growth property for a large class of F-harmonic maps,and obtain a special estimation of F-energy growth,using Hessian comparison theorem in Riemannian geometry.