Geodesic
The Quasi-Additivity Law in conformal geometry
Jeremy Kahn1 ; Mikhail Lyubich1
1 Department of Mathematics<br/>Stony Brook University<br/>Stony Brook, NY 11794<br/>United States<br/>and<br/>Department of Mathematics<br/>University of Toronto<br/>Toronto, Ontario<br/>Canada M5S 2E4
Annals of mathematics, Tome 169 (2009) no. 2, pp. 561-593.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $\partial S$ 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.
DOI : 10.4007/annals.2009.169.561

Jeremy Kahn 1 ; Mikhail Lyubich 1

1 Department of Mathematics<br/>Stony Brook University<br/>Stony Brook, NY 11794<br/>United States<br/>and<br/>Department of Mathematics<br/>University of Toronto<br/>Toronto, Ontario<br/>Canada M5S 2E4 
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Jeremy Kahn; Mikhail Lyubich. The Quasi-Additivity Law in conformal geometry. Annals of mathematics, Tome 169 (2009) no. 2, pp. 561-593. doi : 10.4007/annals.2009.169.561. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.561/

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