HYPERBOLIC GEOMETRIC VERSIONS OF SCHWARZ'S LEMMA

被引：5
作者：
Betsakos, Dimitrios [1 ]
机构：
[1] Aristotle Univ Thessaloniki, Dept Math, Thessaloniki 54124, Greece
来源：
CONFORMAL GEOMETRY AND DYNAMICS | 2013年 / 17卷
关键词：
Holomorphic function; Schwarz lemma; hyperbolic metric; hyperbolic area; hyperbolic capacity; hyperbolic diameter; condenser; symmetrization;
D O I：
10.1090/S1088-4173-2013-00260-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let f be a holomorphic self-map of the unit disk D. We prove monotonicity theorems which involve the hyperbolic area, the hyperbolic capacity, and the hyperbolic diameter of the images under f of hyperbolic disks in D. These theorems lead to distortion and modulus growth theorems that generalize the classical lemma of Schwarz and to geometric estimates for the density of the hyperbolic metric.
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页码：119 / 132
页数：14
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