Deformation of Complex Structures and Boundary Value Problem with Shift

  • G. Akhalaia
  • G. Giorgadze
  • G. Makatsaria
  • N. ManjavidzeEmail author
Part of the Trends in Mathematics book series (TM)


In this paper we consider so called Beltrami parametrization of Riemann surfaces and show that the Riemann-Hilbert boundary value problem with shift is equivalent to classical Riemann-Hilbert boundary value problem with respect to the complex structures defined by Beltrami parametrization induced from shift operator.


Beltrami equation Conformal structure Shift operator Holomorphic bundle Riemann surface 

Mathematics Subject Classification (2010)

Primary 30E25 30G35 Secondary 31A30 



This work was supported by grant N FS 17-96 from the Shota Rustaveli National Science Foundation.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • G. Akhalaia
    • 1
  • G. Giorgadze
    • 1
  • G. Makatsaria
    • 1
  • N. Manjavidze
    • 2
    Email author
  1. 1.I. Vekua Institute of Applied MathematicsTbilisiGeorgia
  2. 2.Ilia State UniversityTbilisiGeorgia

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