Skip to main content
Log in

Explicit Reconstruction of Riemann Surface with Given Boundary in Complex Projective Space

  • Published:
The Journal of Geometric Analysis Aims and scope Submit manuscript

Abstract

In this paper we propose a numerically realizable method for reconstruction of a complex curve with known boundary and without compact components in complex projective space.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Agaltsov, A., Henkin, G.: Algorithm for reconstruction of Riemann surface with given boundary in complex projective space. http://hal.archives-ouvertes.fr/hal-00912925, version 2. 21 March 2014

  2. Chow, W.L.: On compact complex analytic varieties. Am. J. Math. 71(4), 893–914 (1949)

    Article  MATH  Google Scholar 

  3. Darboux, L.: Théorie des surfaces, I, Ch. 10, 2nd edn. Gauthier-Villars, Paris (1914)

    Google Scholar 

  4. Dolbeault, P., Henkin, G.: Surfaces de Riemann de Bord Donné Dans \(\mathbb{C}{\text{ P }}^{n} \), contributions to complex analysis and analytic geometry. Asp. Math. E 26, 163–187 (1994)

    Article  MathSciNet  Google Scholar 

  5. Dolbeault, P., Henkin, G.: Chaines Holomorphes de Bord Donné Dans \(\mathbb{C}{\text{ P }}^{n} \). Bull. Soc. Math. Fr. 125, 383–445 (1997)

    MATH  MathSciNet  Google Scholar 

  6. Harvey, F.R., Lawson, H.: Boundaries of complex analytic varieties. Ann. Math. 102(2), 223–290 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  7. Harvey, F.R., Shiffman, B.: A characterization of holomorphic chains. Ann. Math. 99(3), 553–587 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  8. Henkin, G., Michel, V.: On the explicit reconstruction of a Riemann surface from its Dirichlet–Neumann operator. Geom. Funct. Anal. 17(1), 116–155 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. King, J.: Open problems in geometric function theory. In: Conference on geometric function theory, Katata, p. 4, 1–6 September, Problem D-1 (1978)

  10. Wermer, J.: The hull of a curve in \(\mathbb{C}^n\). Ann. Math. 58(3), 550–561 (1958)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. M. Henkin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agaltsov, A.D., Henkin, G.M. Explicit Reconstruction of Riemann Surface with Given Boundary in Complex Projective Space. J Geom Anal 25, 2450–2473 (2015). https://doi.org/10.1007/s12220-014-9522-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12220-014-9522-1

Keywords

Mathematics Subject Classification

Navigation