Towards the Complexity of Riemann Mappings (Extended Abstract)

d Abstract) Robert Rettinger1 Department of Mathematics and Computer Science University of Hagen, Germany Abstract. We show that under reasonable assumptions there exist Riemann mappings which are as hard as tally -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 -P equals P. Additionally, we give similar results without any assumptions using tally UP instead of -P and show that Riemann mappings of domains with polynomial time computable analytic boundaries are polynomial time computable.

• Type: Conference
• Year: 2009
• Where: CCA
• Authors: Robert Rettinger
• Keywords: CCA 2009, Computable Analytic Boundaries, Polynomial Time, Riemann Mappings, Theoretical Computer Science