Skip to main content
SpringerLink
Log in

Carathéodory Convergence and Harmonic Measure

  • Published:
Potential Analysis Aims and scope Submit manuscript

Abstract

We give several new characterizations of Carathéodory convergence of simply connected domains. We then investigate how different definitions of convergence generalize to the multiply-connected case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Binder, I., Braverman, M., Rojas, C., Yampolsky, M.: Computability of Brolin-Lyubich measure. Comm. Math. Phys. 308(3), 743–771 (2011)

    Article  MathSciNet  Google Scholar 

  2. Binder, I., Braverman, M., Yampolsky, M.: On the computational complexity of the Riemann mapping. Ark. Mat. 45(2), 221–239 (2007)

    Article  MathSciNet  Google Scholar 

  3. Binder, I., Rojas, C., Yampolsky, M.: Computable Carathéodory theory. Adv. Math. 265, 280–312 (2014)

    Article  MathSciNet  Google Scholar 

  4. Carathéodory, C.: Untersuchungen über die konformen Abbildungen von festen und veränderlichen Gebieten. Math. Ann. 72(1), 107–144 (1912)

    Article  MathSciNet  Google Scholar 

  5. Garnett, J.B., Marshall, D.E.: Harmonic Measure. Cambridge University Press (2005)

  6. Hertling, P.: An effective Riemann mapping theorem. Theoret. Comput. Sci. 219(1–2), 225–265 (1999). Computability and complexity in analysis (Castle Dagstuhl, 1997)

    Article  MathSciNet  Google Scholar 

  7. Pommerenke, C.: Univalent functions. Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen, Studia Mathematica/Mathematische Lehrbücher, Band XXV

  8. Pommerenke, Ch.: Uniformly perfect sets and the Poincaré metric. Arch. Math. 32, 192–199 (1979)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

We would like to thank the anonymous referee for helpful comments which served to correct the exposition.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., Toronto, Ontario, M4S 2E4, Canada

    Ilia Binder & Michael Yampolsky

  2. Departmento de Matematicas, Universidad Andres Bello, Republica 498, 2do piso, Santiago, Chile

    Cristobal Rojas

Authors
  1. Ilia Binder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cristobal Rojas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Yampolsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ilia Binder.

Additional information

I. B. was supported in part by an NSERC Discovery grant. M. Y. was supported in part by an NSERC Discovery grnt.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Binder, I., Rojas, C. & Yampolsky, M. Carathéodory Convergence and Harmonic Measure. Potential Anal 51, 499–509 (2019). https://doi.org/10.1007/s11118-018-9721-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11118-018-9721-7

Keywords

Mathematics Subject Classification (2010)

Search

Navigation