On the computational complexity of the Riemann mapping

Arkiv for Matematik

Volumn 45, Issue 2, 2007, Pages 221-239

  Binder, Ilia ^a   Braverman, Mark ^a   Yampolsky, Michael ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38049009611     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11512-007-0045-x     Document Type: Article

References (23)

1. Ahlfors, L. V., Complex Analysis, McGraw-Hill, New York, 1978.
2. Bishop, E. and Bridges, D., Constructive Analysis, Grundlehren Math. Wiss. 279, Springer, Berlin-Heidelberg, 1985.
3. Brattka, V. and Weihrauch, K., Computability on subsets of Euclidean space. I. Closed and compact subsets, Theoret. Comput. Sci. 219 (1999), 65-93.
4. Braverman, M., On the complexity of real functions, in Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (Pittsburgh, PA, 2005), pp. 155-164, IEEE Computer Soc., Washington, DC, 2005.
5. Cheng, H., A constructive Riemann mapping theorem, Pacific J. Math. 44 (1973), 435-454.
6. Chou, A. W., Some complexity issues in complex analysis, in Workshop on Computability and Complexity in Analysis, Informatik-Berichte 190, pp. 91-98, FernUniversität Hagen, Hagen, 1995.
7. Duren, P. L., Univalent Functions, Grundlehren Math. Wiss. 259, Springer, Berlin-Heidelberg, 1983.
8. Furst, M., Saxe, J. B., and Sipser, M., Parity, circuits, and the polynomial-time hierarchy, Math. Systems Theory 17 (1984), 13-27.
9. Garnett, J. B. and Marshall, D. E., Harmonic Measure, New Math. Monogr. 2, Cambridge University Press, Cambridge, 2005.
10. Hertling, P., An effective Riemann mapping theorem, Theoret. Comput. Sci. 219 (1999), 225-265.
11. Koebe, P., Über eine neue methode der konformen abbildung und uniformisierung, Nachr. Königl. Ges. Wiss. Göttingen Math. Phys. Kl. (1912), 844-848.
12. Laasonen, P., On the behavior of the solution of the Dirichlet problem at analytic corners, Ann. Acad. Sci. Fenn. Ser. A. I. 1957:241 (1957), 13 pp.
13. Marshall, D. E., "Zipper", Fortran programs for numerical computation of conformal maps, and C programs for X11 graphics display of the maps, preprint, http://www.math.washington.edu/marshall.
14. Marshall, D. E. and Rohde, S., Convergence of a variant of the Zipper algorithm for conformal mapping, preprint, http://www.math.washington.edu/rohde.
15. Nisan, N., RLSC, Comput. Complexity 4 (1994), 1-11.
16. Papadimitriou, C. H., Computational Complexity, Addison-Wesley, Reading, MA, 1994.
17. Pommerenke, C., Boundary Behaviour of Conformal Maps, Grundlehren Math. Wiss. 299, Springer, Berlin-Heidelberg, 1992.
18. Rettinger, R. and Weihrauch, K., The computational complexity of some Julia sets, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing (San Diego, CA, 2003), pp. 177-185, ACM Press, New York, 2003.
19. Sipser, M., Introduction to the Theory of Computation, Thomson Course Technology, Boston, MA, 2005.
20. Spitzer, F., Principles of Random Walks, Graduate Texts in Math. 34, Springer, Berlin-Heidelberg, 1976.
21. Thurston, W. P., Three-Dimensional Geometry and Topology. Vol. 1, Princeton Math. Ser. 35, Princeton University Press, Princeton, NJ, 1997.
22. Weihrauch, K., Computable Analysis, Texts in Theoretical Computer Science, An EATCS Series, Springer, Berlin-Heidelberg, 2000.
23. Zhou, Q., Computable real-valued functions on recursive open and closed subsets of Euclidean space, Math. Logic Quart. 42 (1996), 379-409.