A Schwarz-Pick inequality for harmonic quasiconformal mappings and its applications

The main result of this paper is the sharp generalized Schwarz-Pick inequality for euclidean harmonic quasiconformal mappings with convex ranges, which generalizes a result given by Mateljevi?. As its applications, we obtain the property of quasi-isometry with respect to the Poincaré distance and an analogue of the Koebe theorem for this class of mappings.     

高维空间的拟正则映照

１引言 众所周知,设Ω是一个复平面区域,则中的Ｂｅｌｔｒａｍｉ方程：的解ｗ＝ｆ（ｚ）称为上的　正则函数,当ｗ＝ｆ（ｚ）是同胚的时候,称为　共形映照．正则函数和什共形映照在复分析中有重要的理论意义和广泛的应用,并已被深入系统的研究［１－５］．如何将它们推广到高维长期受到人们的关注,并已有了一些重要的工作．最近Ｔ．Ｉｗａｎｉｅｃ和Ｇ．Ｍａｒｔｉｎ得到了Ｂｅｌｔｒａｍｉ方程和正则函数的正则性理论在偶数维空间中的相应推广,这是拟正则函数的正则性理论研究中的一个重要发展［６］;之后Ｔ．Ｉｗａｎｉｅｃ应用变…     

Harmonicity of the inverse of a harmonic diffeomorphism

In this paper we obtain a necessary and sufficient condition for the harmonicity of the inverse of a harmonic diffeomorphism. As an application, we give explicit representations of reversible logharmonic diffeomorphisms. As another application, we connect the harmonicity of the inverse of a hyperbolic harmonic quasiconformal diffeomorphism with the Schoen conjecture.     

实验室国家级计量复查认证经验体会

对照《计量认证／审查认可（验收）评审准则》及相关规定，依据评审准则13个要素、56项、126款内容的要求，介绍了对计量认证工作核心问题的理解，计量认证涉及的软、硬件准备工作方面的经验和体会。     

一类非线性椭圆组很弱解的正则性

本文在可控增长条件（1．2）－（14）下,对一类非线性椭圆方程组（1．1）改进其很弱解偏微商的可积性,使其为经典意义下的弱解．     

距离测度空间上的模与容量

1998年,Heinonen和Koskela在文［5］中研究了距离测度空间上的拟共形映照理论.他们所用的最主要的工具之一就是共形模,或称为容量,并给出了一个关于模和容量的不等式,同时他们提出了一个公开的问题在什么条件下不等式中的等号能够成立?本文给出了一些等号能够成立的充分条件.     

On the Discreteness and Convergence in n-Dimensional Mobius Groups

Throughout this paper, we adopt the same notations as in [1,6, 8] such as the Möbius group M(Rⁿ), the Clifford algebraC_n–1, the Clifford matrix group SL(2, _n), the Cliffordnorm of ||A||=(|a|²+|b|²+|c|²+|d|²) (1) and the Clifford metric of SL(2, _n) or of the Möbius groupM(Rⁿ) d(A₁,A₂)=||A₁–A₂||(|a₁–a₂|²+|b₁–b₂|²+|c₁–c₂|²+|d₁–d₂|²)(2) where |·| is the norm of a Clifford number and represents f_i M(), i = 1,2, and so on. In addition, we adopt some notions in [6, 12]:the elementary group, the uniformly bounded torsion, and soon. For example, the definition of the uniformly bounded torsionis as follows.     

(G,H)-拟正则映照和B-调和方程

本文将双特征拟正则映照化为变化问题,得到其Euler-Lasranse方程,利用它得到B-调和方程的先验估计、拟正则映照的Caccippoli型不等式、正则性和可去性结果．     

Truncations of extremal quasiconformal mappings and their applications

In this paper we give a necessary and sufficient condition to decide whether the Teichmüller equivalency class [α] of a truncation α induced by a uniquely extremal Beltrami differential is a Strebel point in T. We also obtain a necessary and sufficient condition of the unique extremality of α. Using the properties of truncations we provide a method to construct Hamilton sequences. We also get a sufficient condition for the extremality of f(z,t) to be equivalent to that of F(w,t). The corresponding results in the infinitesimal case are obtained, too.     

On the compactness of homeomorphisms with integrable dilatations

In this paper, a distortion theorem and some equicontinuity and compactness theorems are obtained for the homeomorphismf with the sphere dilatationH(x,f)∈L _loc(D). Supported by the National Natural Science Foundation of China and the Dctoral Foundation of the Education Commission of China