The order of conformal automorphisms of Riemannian surfaces of infinite type
type: Item
instance of: scholarly article
title: The order of conformal automorphisms of Riemannian surfaces of infinite type
zbMATH Open document ID: 1059.30031
author: Ege Fujikawa
published in: Kodai Mathematical Journal
publication date: 2004-01-28T00:00:00Z
review text: Let \(R\) be a hyperbolic Riemann surface, i.e, the quotient \(R = \mathbb{H}/\Gamma\) where \(\mathbb{H}\) is the upper complex halfplane and \(\Gamma\) is a torsion-free Fuchsian group. Let \(M_R\) be a positive real number greater than the injectivity radius at every point of \(R\). The author shows that the order of any conformal automorphism \(f\) of \(R\) with finite order which fixes a compact subset of \(R\), is upperly bounded by a function depending only on \(M_R\). This result extends to the noncompact case a classical result by Wiman: the order of an automorphism \(f\) of a compact genus \(g\) Riemann surface is upperly bounded by \(2(2g+ 1)\).
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 2034331
zbMATH Keywords: conformal automorphism
zbMATH Keywords: injectivity radius
reviewed by: Jose Manuel Gamboa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1050496645
OpenAlex ID: W1969632145
DOI: 10.2996/KMJ/1050496645
description: scientific article; zbMATH DE number 2034331