Gradient Estimate For Harmonic Maps From Finsler Manifolds To Riemannian Manifolds

In this thesis,we study gradient estimate for harmonic maps from Finsler manifolds to Riemannian manifolds.As an application,we obtain Liouville type theorem of harmonic maps from a weak Landsberg manifold to a Cartan-Hadamard manifold.Moreover,we generalize the Liouville type theorem to a regular ball of Riemannian manifold.The main contents of this thesis are as follows:In the first chapter,we introduce research background and status of Finsler Geometry and harmonic maps,then we describe the main results,possible innovation and deficiency of the thesis.In the second chapter,we firstly introduce the basic knowledge of Finsler Geometry and harmonic maps;secondly,we give some lemmas including the proof of Maximum principle of the horizontal Laplacian;at last,we give the definition of the comparison theorem function and an example about it.In the third chapter,we will deduce the Bochner formula in two cases by using the local coordinates and some related theorems.In the last chapter the proof of the main theorems are given.We construct the auxiliary function and use the Bochner formula and Maximum principle to prove the theorems.