On Hyperbolic Metric and Invariant Beltrami Differentials for Rational Maps

被引：1
|
作者：
Cabrera, Carlos [1 ]
Makienko, Peter [1 ]
机构：
[1] UNAM, Inst Matemat, Unidad Cuernavaca, Cuernavaca, Morelos, Mexico
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2018年 / 28卷 / 03期
关键词：
Rational maps; hyperbolic metric; Teichmuller space;
D O I：
10.1007/s12220-017-9906-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a rational map R, we consider the complement of the postcritical set . In this paper we discuss the existence of invariant Beltrami differentials supported on an R invariant subset X of . Under some geometrical restrictions on X, we show the absence of invariant Beltrami differentials with support intersecting X. In particular, we show that if X has finite hyperbolic area, then X cannot support invariant Beltrami differentials except in the case where R is a LattSs map.
引用
收藏
页码：2346 / 2360
页数：15
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