Abstract |
|
On a Riemann surface S of finite 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
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.
|
Mathematical Subject Classification
Primary: 37F45
|
Authors
|
