Some Results On F-Harmonic Maps

In this thesis,we mainly study the stable F -harmonic maps and the gap property of F -harmonic maps and the Liouville-type theorem on exponential-harmonic maps,then obtain some results.In chapter 1,we will make a general description on the recent researches in our field.In chapter 2, we introduce the preliminaries for the paper.In chapter3,we investigate the stable F -harmonic maps from or into general subma -nifolds of the sphere and the Euclidean space. Assuming that all initial manifolds are compact,we prove that this stable F -harmonic map is constant,if the Ricci curvature of the submanifold has some lower bound and F"≤0 .In chapter 4, we establish a Bochner-typed formula and use it to study the gap property of F -harmonic maps, then obtain a pointwise quantum theorem.In chapter 5, we discuss the constant boundary-valued problems for exponential -harmonic maps on complete simply connected Riemannian manifolds with negative sectional curvature, and obtains Liouville-type theorems.