Skip to main content
SpringerLink
Log in

Corrections and complements to “Once-holed tori embedded in Riemann surfaces”

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

Abstract

Once-holed tori are the most primitive noncompact Riemann surfaces of positive genus, and can be used to measure the sizes of handles of Riemann surfaces of positive genus. We study some families of once-holed tori that are conformally embedded in target Riemann surfaces of conformal mappings of a given noncompact Riemann surface of genus one, and correct some results given in Masumoto (Math. Z. 257:453–464, 2007).

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. Ahlfors L.V., Sario L.: Riemann Surfaces. Princeton University Press, Princeton (1960)

    MATH  Google Scholar 

  2. Masumoto M.: On the moduli set of continuations of an open Riemann surface of genus one. J. Anal. Math. 63, 287–301 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Masumoto M.: Conformal mappings of a once-holed torus. J. Anal. Math. 66, 117–136 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Masumoto M.: Once-holed tori embedded in Riemann surfaces. Math. Z. 257, 453–464 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Shiba M.: The moduli of compact continuations of an open Riemann surface of genus one. Trans. Am. Math. Soc. 301, 299–311 (1987)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yamaguchi University, Yamaguchi, 753-8512, Japan

    Makoto Masumoto

Authors
  1. Makoto Masumoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Makoto Masumoto.

Additional information

Supported in part by JSPS KAKENHI 19540187.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Masumoto, M. Corrections and complements to “Once-holed tori embedded in Riemann surfaces”. Math. Z. 267, 869–874 (2011). https://doi.org/10.1007/s00209-009-0650-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-009-0650-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation