Factorisation of conformal maps on finitely connected domains

2011/07/04 by Benjamin Doyon, Doyon, Benjamin · 2 citations
Mathematics · #Analytic and geometric function theory #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.CV

paper · pdf · doi:10.48550/arxiv.1107.0582

5 pages

arxiv created 2011/07/04 · arxiv updated 2011/07/05

Abstract

Let U be a multiply connected domain of the Riemann sphere C whose complement C∖ U has N<∞ components. We show that every conformal map on U can be written as a composition of N maps conformal on simply connected domains. This improves on a recent result of D.E. Marshall, but our proof uses different ideas, and involves the uniformisation theorem for Riemann surfaces.

Cited by

• Higher conformal variations and the Virasoro vertex operator algebra
• Random conformal welding for finitely connected regions

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