|本期目录/Table of Contents|

[1]贾改莉,张孝惠.三角比度量的界和比较不等式[J].浙江理工大学学报,2020,43-44(自科六):858-864.
　JIA Gaili,ZHANG Xiaohui.Bounds and comparison inequalities for  the triangular ratio metric[J].Journal of Zhejiang Sci-Tech University,2020,43-44(自科六):858-864.
点击复制

三角比度量的界和比较不等式()
分享到：

浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第43-44卷
期数:
2020年自科六期
页码:
858-864
栏目:
出版日期:
2020-11-27

文章信息/Info

Title:
Bounds and comparison inequalities for  the triangular ratio metric
文章编号:
1673-3851 (2020) 11-0858-07
作者:
贾改莉; 张孝惠
浙江理工大学理学院，杭州 310018
Author(s):
JIA Gaili;  ZHANG Xiaohui
School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
三角比度量; 双曲型度量; 凸域
分类号:
O174-5
文献标志码:
A
摘要:
研究了三角比度量在单位圆盘内的上下界，分别证明了三角比度量与距离比度量、双曲度量、Cassini度量 和 Gromov双曲度量等四个度量的比较关系。特别地，证明了三角比度量与这些双曲型度量之间不等式的精确性。

参考文献/References:

［1］ Klén R, Lindén H, Vuorinen M, et al. The visual angle metric and Mbius transformations［J］. Computational Methods and Function Theory, 2014, 14(2/3): 577-608.
［2］ Chen J L, Hariri P, Klén R, et al. Lipschitz conditions, triangular ratio metric, and quasiconformal maps［J］. Annales Academiae Scientiarum Fennicae Mathematica, 2015, 40: 683-709.
［3］ Hariri P, Vuorinen M, Zhang X H. Inequalities and biLipschitz conditions for the triangular ratio metric［J］. Rocky Mountain Journal of Mathematics, 2017, 47(4): 1121-1148.
［4］ Beardon A F. The Geometry of Discrete Groups［M］. New York: Springer, 1983: 40.
［5］ Vuorinen M. Conformal invariants and quasiregular mappings［J］. Journal D’Analyse Mathématique, 1985, 45: 69-115.
［6］ Gehring F W, Osgood B G. Uniform domains and the quasihyperbolic metric［J］. Journal d’Analyse Mathématique, 1979, 36: 50-74.
［7］ Gehring F W, Palka B P. Quasiconformally homogeneous domains［J］. Journal D’Analyse Mathématique, 1976, 30: 172-199.
［8］ Vuorinen M. Conformal Geometry and Quasiregular Mappings［M］. Berlin: Springer, 1988: 29.
［9］ Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Maps［M］. New York: John Wiley ＆ Sons,1997: 151.
［10］ Ibragimov Z. The Cassinian metric of a domain in Rn［J］. Uzbekskiǐ Matematicheskiǐ Zhurnal, 2009(1): 53-67.

相似文献/References:

[1]许小雪,王根娣.伸缩不变Cassini度量的精确不等式[J].浙江理工大学学报,2019,41-42(自科六):829.
　XU Xiaoxue,WANG Gendi.Sharp inequalities for the scale invariant Cassinian metric[J].Journal of Zhejiang Sci-Tech University,2019,41-42(自科六):829.

备注/Memo

备注/Memo:
收稿日期：2020-06-26
Published Online：2020-09-03
基金项目：This research is supported by National Natural Science Foundation of China (NNSFC) (Grant No.11771400)and Science Foundation of Zhejiang Sci-Tech University (ZSTU) (Grant No.16062023-Y)
作者简介：JIA Gaili (1993- ),female, Datong, Shanxi,postgraduate,research interests: complex analysis
通信作者：ZHANG Xiaohui, E-mail: xiaohui.zhang@zstu.edu.cn
更新日期/Last Update: 2020-11-05