Work

Weil–Petersson class non-overlapping mappings into a Riemann surface

Year: 2015

Type: article

Abstract: For a compact Riemann surface of genus [Formula: see text] with [Formula: see text] punctures, consider the class of [Formula: see text]-tuples of conformal mappings [Formula: see text] of the unit disk each taking [Formula: see text] to a puncture. Assume further that (1) these maps are quasiconformally extendible to [Formula: see text], (2) the pre-Schwarzian of each [Formula: see text] is in the Bergman space, and (3) the images of the closures of the disk do not intersect. We show that the class of such non-overlapping mappings is a complex Hilbert manifold.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199715500601

Authors: David Radnell, Eric Schippers, Wolfgang Staubach

Institutions: Aalto University, University of Manitoba, Uppsala University

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2159034603

FWCI: 3.366

Cites: 32

Cited by: 10

Related to: 10