f-Harmonic maps of doubly warped product manifolds

In this paper, we study f-harmonicity of some special maps from or into a doubly warped product manifold. First we recall some properties of doubly twisted product manifolds. After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M × _μ,λ N can not be proper f-harmonic maps, we use projection maps and product maps to construct nontrivial f-harmonic maps. Thus we obtain some similar results given in [21], such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps. Furthermore, we investigate non-trivial f-harmonicity of the product of two harmonic maps.     

多值函数在复变函数中的应用

通过讨论初等多值函数的单值解析分枝问题,重点研究了初等多值函数在复变函数中的具体应用.     

保形映射的一个应用——大岩心水平渗透率公式

本文利用流函数满足 Laplace方程在保形映射下不变的性质 ,给出了渗透率公式     

奇异黎曼度量之下分支问题的C0接触等价D决定性

本文使用奇点理论方法对奇异黎曼度量之下的分支问题进行了拓扑性质的研究,给出了分支问题中的C     

The Energy Growth Property for Harmonic Maps

Ｔｈｅ　Ｅｎｅｒｇｙ　Ｇｒｏｗｔｈ　Ｐｒｏｐｅｒｔｙ　ｆｏｒ　Ｈａｒｍｏｎｉｃ　ＭａｐｓＴｈｅＥｎｅｒｇｙＧｒｏｗｔｈＰｒｏｐｅｒｔｙｆｏｒＨａｒｍｏｎｉｃＭａｐｓ￥ＬｉＨｏｎｇｙｉ；ＺｈａｏＤｉ（ＮｏｒｔｈＣｈｉｎａｉｎｓｔｉｔｕｔｅｏｆＷａｔｅｒ...     

具有非负Ricci曲率和次大体积增长的完备流形(英文)

本文研究了具有非负Ricci曲率和次大体积增长的完备黎曼流形的拓扑结构问题.利用Toponogov型比较定理及临界点理论,获得了流形具有有限拓扑型的结果,推广了H.Zhan和Z.Shen的定理,并且还证明了该流形的基本群是有限生成的.     

Remarks on Thurston’s Construction of Pseudo-Anosov Maps of Riemann Surfaces

It is well known that certain isotopy classes of oseudo-Anosov maos on a Riemann surface S of non-excluded type can be defined through Dehn twists tα and tβ along simple closed geodesics α and β on S,respectively. Let G be the corresponding Fuchsian group acting on the hyperbolic plane H so that H/G≌S.For any point α∈S,define S = S／{α}.In this article, the author gives explicit parabolic elements of G from which he constructs pseudo-Anosov classes on S that can be projected to a given pseudo-Anosov class on S obtained from Thurston＇s construction.     

Generating Quadratic Pseudo-Anosov Homeomorphisms of Closed Surfaces

In this note, we show that given a closed, orientable genus-g surface S _g , any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S _g . To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism.     

An isomorphism theorem for Teichmüller curves

It is proved that for any Fuchsian group Г such that H/Г is a hyperbolic Riemann surface, the Teichmuller curve V(Г) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Г) onto V(Г) is holomorphic with local holomorphic sections. An isomorphism theorem for Teichmuller curves is deduced, which generalizes a classical result that the Teichmuller curve V(Г) depends only on the type of Г and not on the orders of the elliptic elements of Г when H/Г is a compact hyperbolic Riemann surface.