The Quasi-Additivity Law in conformal geometry
成果类型：
Article
署名作者：
Kahn, Jeremy; Lyubich, Mikahil
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2009.169.561
发表日期：
2009
页码：
561-593
关键词：
摘要：
On a Riemann surface S of finite type containing a family of N disjoint disks D-i (islands), we consider several natural conformal invariants measuring the distance from the islands to partial derivative S and the separation between different islands. In a near degenerate situation we establish a relation between them called the Quasi-Additivity Law. We then generalize it to a Quasi-Invariance Law providing us with a transformation rule of the moduli in question under covering maps. This rule (and in particular, its special case called the Covering Lemma) has important applications in holomorphic dynamics.