When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.CCA.2009.2272
URN: urn:nbn:de:0030-drops-22724
URL: https://drops.dagstuhl.de/opus/volltexte/2009/2272/
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Rettinger, Robert
Contributed Papers

### Towards the Complexity of Riemann Mappings (Extended Abstract)

 pdf-format:

### Abstract

We show that under reasonable assumptions there exist Riemann mappings which are as hard as tally \$\sharp\$-P even in the non-uniform case. More precisely, we show that under a widely accepted conjecture from numerical mathematics there exist single domains with simple, i.e. polynomial time computable, smooth boundary whose Riemann mapping is polynomial time computable if and only if tally \$\sharp\$-P equals P. Additionally, we give similar results without any assumptions using tally \$UP\$ instead of \$\sharp\$-P and show that Riemann mappings of domains with polynomial time computable analytic boundaries are polynomial time computable.

### BibTeX - Entry

```@InProceedings{rettinger:OASIcs:2009:2272,
author =	{Robert Rettinger},
title =	{{Towards the Complexity of Riemann Mappings  (Extended Abstract)}},
booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
series =	{OpenAccess Series in Informatics (OASIcs)},
ISBN =	{978-3-939897-12-5},
ISSN =	{2190-6807},
year =	{2009},
volume =	{11},
editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},