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

Towards the Complexity of Riemann Mappings (Extended Abstract)

pdf-format:
Dokument 1.pdf (353 KB)

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:DSP:2009:2272,
  author =	{Robert Rettinger},
  title =	{Towards the Complexity of Riemann Mappings  (Extended Abstract)},
  booktitle =	{6th Int'l Conf. on Computability and Complexity in Analysis},
  year =	{2009},
  editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2272},
  annote =	{Keywords: Riemann mapping, complexity, polynomial time},
}

Keywords: Riemann mapping, complexity, polynomial time
Seminar: 6th International Conference on Computability and Complexity in Analysis (CCA'09)
Issue date: 2009
Date of publication: 25.11.2009

DROPS-Home | Fulltext Search | Imprint Published by LZI