Computable Riemann Surfaces

(Extended Abstract)
  • Robert Rettinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

Abstract

In this paper we introduce computable and time bounded Riemann surfaces, based on the classical abstract definition by charts. Building upon this definition we discuss computable versions of several classical results, such as the existence of complete continuations of holomorphic functions, universal coverings and the uniformization theorem (for some cases).

Though we state most of our results for computable surfaces, many of them can also be transformed to a uniform version, i.e. based on representations of the class of Riemann surfaces (modulo conformal equivalence).

Keywords

computable Riemann surface computable uniformization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Robert Rettinger
    • 1
  1. 1.FernUniversität Hagen, LG Komplexität und Algorithmen, Universitätsstrasse 1, D-58095 Hagen 

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