Compactness and the effectivity of uniformization

Authors:
Robert Rettinger
Affiliations:
Fakultät für Mathematik und Informatik, FernUniversität in Hagen, Hagen, Germany
Venue:
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Year:
2012

Citing 6
Cited 0

Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions

Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Uniform computational complexity of Taylor series

14th International Colloquium on Automata, languages and programming
An effective Riemann mapping theorem

Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction

Computable analysis: an introduction
Computability on subsets of metric spaces

Theoretical Computer Science - Topology in computer science
Lower Bounds on the Continuation of Holomorphic Functions

Electronic Notes in Theoretical Computer Science (ENTCS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give new proofs of effective versions of the Riemann mapping theorem, its extension to multiply connected domains and the uniformization on Riemann surfaces. Astonishingly, in the presented proofs we need barely more than computational compactness and the classical results.