Some Results Of F-harmonic Maps

In this paper, we mainly discuss the stability and constant boundary-value problem of F-harmonic maps. If the target manifold holds a convex function, we discuss the weak F-harmonic map between Riemannian manifolds. This paper is made up of five parts:In chapter one, we introduce the background and investigation meaning of F-harmonic maps. Furthermore, we show the relevant research progress, what's more, we state our three main problems.In chapter two, we give the definition of F-harmonic maps and some basic results. We also give other definitions which are used in the paper.In chapter three, we discuss the stability of F-harmonic maps, and generalize Li Jintang and Ohnita's results.In chapter four, we study constant boundary-value problems for F-harmonic maps on complete simply connected Riemannian manifolds with nonpositive sectional curvature, and obtain Liouville type theorems.In chapter five, Weak F-harmonic maps between Riemannian manifolds are investigated. Some theorems of Liouville type are given for such maps when target manifolds have convex functions.