Abstract
On a Riemann surface S of nite type containing a family of N disjoint disks Di (\islands), we consider several natural conformal invariants measuring the distance from the islands to @S and the separation between dierent 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.
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