Can I read The Quasi-Additivity Law in Conformal Geometry on EtoBox?

The Quasi-Additivity Law in Conformal Geometry by Kahn, Jeremy; Lyubich, Mikhail is a scholarly article available to read on EtoBox.

What is The Quasi-Additivity Law in Conformal Geometry about?

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 $\di S$ and 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 which will be addressed in the forthcoming notes.

Author

Kahn, Jeremy; Lyubich, Mikhail

Published

2005

Language

EN