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On the \(\bar \partial\)-problem with L 2-estimates on a Riemann surface

  • E. M. Chirka
Article

Abstract

The L 2-estimates obtained by Hörmander for the solutions to the \(\bar \partial\)-problem are specified and complemented in the simplest one-dimensional case of Riemann surfaces.

Keywords

Riemann Surface STEKLOV Institute Curvature Form Subharmonic Function Holomorphic Line Bundle 
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References

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    R. C. Ganning and R. Narasimhan, “Immersion of open Riemann surfaces,” Math. Ann. 174, 103–108 (1967).MATHMathSciNetCrossRefGoogle Scholar
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    H. Hedenmalm, “On Hörmander’s solution of the ā-equation,” arXiv: 1311.2020 [math.AP].Google Scholar
  3. 3.
    L. Hörmander, Notions of Convexity (Birkhäuser, Boston, MA, 1994), Prog. Math. 127.Google Scholar
  4. 4.
    T. Napier and M. Ramachandran, An Introduction to Riemann Surfaces (Springer, New York, 2011).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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