Conformal mappings of a once-holed torus
type: Item
instance of: scholarly article
title: Conformal mappings of a once-holed torus
zbMATH Open document ID: 0842.30034
DOI: 10.1007/BF02788820
author: Makoto Masumoto
published in: Journal d'Analyse Mathématique
publication date: 1996-05-21T00:00:00Z
review text: \textit{M. Shiba} showed [Trans. Am. Math. Soc. 301, 299-311 (1987; Zbl 0626.30046)] that the set of moduli of marked tori into which a given marked open Riemann surface can be embedded is precisely a closed disk in the upper half plane. The author uses this result to solve the problem whether a once-holed torus can be conformally embedded into another or not. Moreover, he gives a new set of moduli for the Teichmüller space of a once-holed torus and describes the action of the modular group on the Teichmüller space. The problem to relate the new set of moduli to ones introduced before seems to be difficult.
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 854439
zbMATH Keywords: Teichmüller space
reviewed by: Steffen Timmann
MaRDI profile type: Publication
cites work: Q3282112
cites work: Q5512337
cites work: Q3665386
cites work: Q5593095
cites work: Q3310101
cites work: Reduced Teichmuller Spaces
cites work: Q3766016
cites work: Extremal length geometry of teichmüller space
cites work: Q4061209
cites work: Moduli of Punctured Tori and the Accessory Parameter of Lame's Equation
cites work: Pleating coordinates for the Maskit embedding of the Teichmüller space of punctured tori
cites work: The asymptotic geometry of Teichmüller space
cites work: Q3744437
cites work: The heights theorem for quadraic differentials on Riemann surfaces
cites work: Estimates of the euclidean span for an open Riemann surface of genus one
cites work: On the moduli set of continuations of an open Riemann surface of genus one
cites work: Q3994371
cites work: The Moduli of Compact Continuations of an Open Riemann Surface of Genus One
cites work: Q3798945
cites work: Q4731436
description: scientific article; zbMATH DE number 854439