Rn中单位球上满足Poisson方程的边界Schwarz引理

Schwarz引理在全纯映射和调和映射理论中扮演着重要的角色.本文建立了Rn中单位球上满足Poisson方程解的边界Schwarz引理.作为应用,给出了单位球上调和自映射的边界Schwarz引理,将平面上的多重调映射结果和边界Schwarz引理推广到了高维调和映射.     

边界型Schwarz引理

Schwarz引理是复分析中最重要的定理之一,本文给出了边界型Schwarz引理.     

Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广

对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计.     

Schwarz引理的推广及其应用

引入Schwarz引理的一个最常见的推广定理,并且作出了详细的证明.同时以引理形式介绍了一个实用的复数性质,并且利用这两个引理,给出了开圆盘内解析函数的的实部,虚部以及模的估计式.     

Hermitian调和映照的Schwarz引理

由Jost和Yau引进的Hermitian调和映照是Riemannian流形上通常的调和映照在Hermitian流形上的一种自然的类比.本文证明了复分析中经典的Schwarz引理对一大类Hermitian调和映照仍然成立.作为推论,我们得到了半共形Hermitian调和映照的Liouville性质.     

解析算子函数的Schwarz引理的一般形式

该文对Ｆａｎ＾「２」和Ｍｉｓｈｒａ＾「３」关于算子情形的Ｓｃｈｗａｒｚ引理作了进一步的延拓，使其结果对于解析算子函数仍然成立。     

拟凸域上沿某些方向的边界 Schwarz 引理*

本文直接利用全纯映照的性质研究边界Schwarz引理,建立了拟凸域上沿某些满足正定条件的方向的边界Schwarz引理. 文章推广了强拟凸域情形的主要结果,但是证明的方法是不一样的.     

单位球上α次准凸映射精细的偏差定理

利用欧氏空间单位球的边界型Schwarz引理给出α次准凸映射在极值点处精细的行列式型偏差定理和矩阵型偏差定理.     

单位球上星形映射在极值点处的偏差定理

利用多复变数的边界型Schwarz引理,建立了C~n中单位球上正规化双全纯星形映射在极值点处的行列式型偏差定理和矩阵型偏差定理.     

Frink-Tukey度量化引理

一致空间的度量化问题是一致空间的基本问题之一,其主要工具是Tukey度量化引理.证明在拓扑空间的度量化问题中起主要工具之一的Frink引理与Tukey度量化引理如出一辙,可将它们称之为Frink-Tukey度量化引理.     

一个Schwarz引理的推广（英文）

In this paper, we establish a boundary Schwarz Lemma for holomorphic mapping on the generalized complex ellipsoid in C~n.     

A Generalized Schwarz Lemma

In this paper,we establish a boundary Schwarz Lemma for holomorphic mapping on the generalized complex ellipsoid in Cn.     

Dirichlet Problem,Univalency and Schwarz Lemma for Biharmonic Mappings

In this paper, we shall discuss the family of biharmonic mappings for which the maximum principle holds. As a consequence of our study, we present Schwarz Lemma for certain class of biharmonic mappings. Also we discuss the univalency of certain class of biharmonic mappings.     

Two isoperimetric inequalities for the Sobolev constant

In this note, we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalizes an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.     

Landau定理中上界的一个改进

通过相关文献给出的穿孔平面C\{0,1}的双曲度量的密度函数的新的下界估计,借助广义Schwarz引理我们对Landau定理中关于上界做了进一步改进并得到了一个带参数的上界表达式.并且当参数取到0时,此结论正好为相关文献得到的结果.     

Schwarz Lemma in infinite-dimensional spaces

We state and prove an extension of the Schwarz Lemma that involves infinite-dimensional spaces. Our generalized version contains some known variations of this classical result in geometric function theory. We derive our extension in the context of the Minkowski functional.     

A multidimensional real Schwarz Lemma for the Hilbert metric

We present a real multidimensional version of the Schwarz Lemma on a bounded convex domain D of ℝ ⁿ endowed with the Hilbert metric. We provide as an application an extension of a Birkhoff’s Theorem on mappings contracting the Hilbert metric.     

Some generalizations of Ahlfors Lemma

One of the most influential versions of the classical Schwarz–Pick Lemma is probably that of Ahlfors. Pulling back a conformal semimetric on a Riemann surface under any holomorphic map from the open unit disk equipped with a Poincaré metric, the curvature of which is assumed to bound from above the curvature of the Riemann surface, he successfully showed that a conformal semimetric to be compared with the Poincaré metric is obtained. In the present paper, we give a comparison theorem between two conformal semimetrics of variable curvature in the same spirit. Our main theorem is a local one by its nature, but global results can be derived therefrom.     

Modular equations and distortion functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky’s Theorem. These results also yield new bounds for singular values of complete elliptic integrals.