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…     

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。     

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.     

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．     

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     

A note on harmonic quasiconformal mappings

In this note we show that a harmonic quasiconformal mapping f=u+iv with respect to the Poincaré metric of the upper half plane onto itself such that v(x,y)=v(y) or u(x,y)=u(x) is a conformal mapping.     

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.     

拟正则映照的局部单叶性和VMO_Φ空间的Orlicz-范数

本文证明了如果拟正则映照f的伸张张量Gf（x）或矩阵伸张Mf（x）与VMOφ空间的Orlicz-范数距离充分小,则f为局部同胚.     

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.