Skip to main content
×
×
Home

Effective Riemann mappings of multiply connected domains and Riemann surfaces

  • ROBERT RETTINGER (a1) (a2)
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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Effective Riemann mappings of multiply connected domains and Riemann surfaces
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Effective Riemann mappings of multiply connected domains and Riemann surfaces
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Effective Riemann mappings of multiply connected domains and Riemann surfaces
      Available formats
      ×
Copyright
References
Hide All
Abikoff, W. (1981). The uniformization theorem. The American Mathemtical Monthly 88 (8) 574592.
Ahlfors, L. (1979). Complex Analysis, 3rd ed. McGraw-Hill Science/Engineering/Math.
Andreev, V. and McNicholl, T. (2009). Computing conformal maps onto canonical slit domains. In: Proceedings of the 6th International Conference on Computability and Complexity in Analysis, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany 2536.
Binder, I., Braverman, M. and Yampolsky, M. (2007). On computational complexity of Riemann mapping. Arkiv for Matematik 45 (2) 221239.
Brattka, V. and Presser, G. (2003). Computability on subsets of metric spaces. Theoretical Computer Science 305 (1–3) 4376.
Galatolo, S., Hoyrup, M. and Rojas, C. (2011). Dynamics and abstract computability: Computing invariant measures. Discrete and Continuous Dynamical Systems 29 (1) 193212.
Henrici, P. (1986). Applied and Computational Complex Analysis, Vol. 3, Wiley Classics Library Series.
Hertling, P. (1999). An effective Riemann mapping theorem. Theoretical Computer Science 219 (1–2) 225265.
Müller, N. (1987). Uniform computational complexity of Taylor series. In: ICALP 87. Springer-Verlag Lecture Notes in Computer Science 267 435444.
Nehari, Z. (1952). Conformal Mapping, McGraw-Hill.
Rettinger, R. (2008). Lower bounds on the continuation of holomorphic functions. Electronic Notes in Theoretical Computer Science 221 207217.
Rettinger, R. and Weihrauch, K. (2013). Products of effective topological spaces and a uniformly computable Tychonoff Theorem. Logical Methods in Computer Science 9 (4) 414.
Weihrauch, K. (2000). Computable Analysis, Springer.
Weihrauch, K. (2008). The computable multi-functions on multi-represented sets are closed under programming. Journal of Universal Computer Science 14 (6) 801844.
Weihrauch, K. and Grubba, T. (2009). Elementary computational topology. Journal of Universal Computer Science 15 (6) 13811422.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×