[1]陈行堤,黄心中.拟共形映照的爆破集问题[J].华侨大学学报(自然科学版),2001,22(2):111-116.[doi:10.3969/j.issn.1000-5013.2001.02.001]
　Chen Xingdi,Huang Xinzhong.Explodable Set of Quasiconformal Mapping[J].Journal of Huaqiao University(Natural Science),2001,22(2):111-116.[doi:10.3969/j.issn.1000-5013.2001.02.001]
点击复制

拟共形映照的爆破集问题()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第22卷
期数:
2001年第2期
页码:
111-116
栏目:
出版日期:
2001-04-20

文章信息/Info

Title:
Explodable Set of Quasiconformal Mapping
文章编号:
1000-5013(2001)02-0111-06
作者:
陈行堤; 黄心中
华侨大学经济管理学院, 泉州362011
Author(s):
Chen Xingdi;  Huang Xinzhong
College of Econ. Manag., Huaqiao Univ., 362011, Quanzhou
关键词:
拟共形映照;  双曲几何;  爆破集;  径向映照;  偏差定理
Keywords:
quasiconformal mapping;  hyperbolic geometry;  explodable set;  radial mapping;  distortion theorem
分类号:
O174.55
DOI:
10.3969/j.issn.1000-5013.2001.02.001
摘要:
研究平面拟共形映照的爆破集性质 .找到了判别平面集合的双曲面积为无限的一个充分条件,对径向 K-拟共形映照的双曲面积进行估计,改进了近期由 Porter和 Reséndis所得到的相应结果 .
Abstract:
In relation to explodable set of quasiconformal mapping, the author studies its properties; and finds a sufficient condition for judging hyperbolic area of a set on a plane to be infinite; and estimates hyperbolic area of radial K quasiconformal mapping; and improves corresponding results obtained recently by Porter and Reséndis.

参考文献/References:

[1] Mori A. On quasi-conformality and pseudo-analyticity [J]. Transactions of the American Mathematical Society, 1957.57-77.
[2] Gehring F W, Reich E. Area distortion under quasiconformal mappings [J]. Annales Academic Scientiarum Fennicae Mathematica, 1966.1-14.
[3] BOJARSKI B. Generalized solutions of a system of differential equations of first order and elliptic type with discontinuous coefficients [J]. Math Sbornik, 1957.451-503.
[4] Astala K. Area distortion of quasiconformal mappings [J]. Annales Academic Scientiarum Fennicae Mathematica, 1966.1-14.
[5] Eremenko A, Hamilton D H. On the area distortion by quasiconformal mappings [J]. Proceedings of the American Mathematical Society, 1995.2793-2797.
[6] Porter R M, Reséndis L F. Quasiconformally explodable sets [J]. Complex Variables, 1998.379-392.

相似文献/References:

[1]赖万才.拟共形映照的模数偏差[J].华侨大学学报(自然科学版),1985,6(2):141.[doi:10.11830/ISSN.1000-5013.1985.02.0141]
　Lai Wancai.On the Distortion of Modulus of Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),1985,6(2):141.[doi:10.11830/ISSN.1000-5013.1985.02.0141]
[2]赖万才.拟共形映照的一个极值问题[J].华侨大学学报(自然科学版),1989,10(4):359.[doi:10.11830/ISSN.1000-5013.1989.04.0359]
　Lai Wancai.An Extremal Problem for Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),1989,10(2):359.[doi:10.11830/ISSN.1000-5013.1989.04.0359]
[3]黄心中.参数表示下的拟共形映照[J].华侨大学学报(自然科学版),1997,18(2):111.[doi:10.11830/ISSN.1000-5013.1997.02.0111]
　Huang Xinzhong.Quasiconformal Mappings with Parametric Representation[J].Journal of Huaqiao University(Natural Science),1997,18(2):111.[doi:10.11830/ISSN.1000-5013.1997.02.0111]
[4]黄心中.分段与整体拟对称函数之间的关系[J].华侨大学学报(自然科学版),1999,20(1):1.[doi:10.11830/ISSN.1000-5013.1999.01.0001]
　Huang Xinzhong.Relation between Piecewise and Global Quasi Symmetric Functions[J].Journal of Huaqiao University(Natural Science),1999,20(2):1.[doi:10.11830/ISSN.1000-5013.1999.01.0001]
[5]刘金雄.Reich的一个定理改进及其相关问题[J].华侨大学学报(自然科学版),2000,21(1):8.[doi:10.3969/j.issn.1000-5013.2000.01.002]
　Liu Jinxiong.Improving One of Reich’s Theorems and Problem Correlated with It[J].Journal of Huaqiao University(Natural Science),2000,21(2):8.[doi:10.3969/j.issn.1000-5013.2000.01.002]
[6]刘金雄.一类唯一极值Teichmǖller映照的判别法[J].华侨大学学报(自然科学版),2000,21(4):331.[doi:10.3969/j.issn.1000-5013.2000.04.001]
　Liu Jinxiong.Criterion for a Class of Uniquely Extremal Teichmüller Mappings[J].Journal of Huaqiao University(Natural Science),2000,21(2):331.[doi:10.3969/j.issn.1000-5013.2000.04.001]
[7]刘金雄.一类唯一极值Teichmller映照的存在性[J].华侨大学学报(自然科学版),2001,22(1):6.[doi:10.3969/j.issn.1000-5013.2001.01.002]
　Liu Jinxiong.Existence of a Class of Uniquely Extremal Teichmller Mappings[J].Journal of Huaqiao University(Natural Science),2001,22(2):6.[doi:10.3969/j.issn.1000-5013.2001.01.002]
[8]林峰.Beurling-Ahlfors扩张的伸张函数的边界极限[J].华侨大学学报(自然科学版),2004,25(4):352.[doi:10.3969/j.issn.1000-5013.2004.04.004]
　Lin Feng.Boundary Limit of Dilatation Function of Beurling-Ahlfors Extension[J].Journal of Huaqiao University(Natural Science),2004,25(2):352.[doi:10.3969/j.issn.1000-5013.2004.04.004]
[9]朱剑锋,黄心中.区间上拟对称函数的延拓定理[J].华侨大学学报(自然科学版),2007,28(1):83.[doi:10.3969/j.issn.1000-5013.2007.01.022]
　ZHU Jian-feng,HUANG Xin-zhong.The Extension Theorem of Quasisymmetric Function on the Interval[J].Journal of Huaqiao University(Natural Science),2007,28(2):83.[doi:10.3969/j.issn.1000-5013.2007.01.022]
[10]韩雪,黄心中.拟共形映照的双曲面积偏差[J].华侨大学学报(自然科学版),2007,28(4):433.[doi:10.3969/j.issn.1000-5013.2007.04.026]
　HAN Xue,HUANG Xin-zhong.Hyperbolic Area Distortion under Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),2007,28(2):433.[doi:10.3969/j.issn.1000-5013.2007.04.026]

备注/Memo

备注/Memo:
福建省自然科学基金
更新日期/Last Update: 2014-03-23