Deformation of Complex Structures and Boundary Value Problem with Shift
- 335 Downloads
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.
KeywordsBeltrami 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.
- 1.G. Akhalaia, G. Giorgadze, V. Jikia, N. Kaldani, N. Manjavidze, G. Makatsaria, Elliptic systems on Riemann surfaces. Lecture Notes of TICMI, vol. 13, pp. 1–147. Tbilisi University Press, Tbilisi (2012)Google Scholar
- 4.B. Bojarski, On a boundary value problem for a system of elliptic equations. Dokl. Akad. Nauk SSSR (N.S.) 102, 201–204 (1955)Google Scholar
- 11.G. Manjavidze, Boundary-value problems with conjugation for generalized analytic functions, in Proceedings of the I. Vekua Institute of Applied Mathematics (Tbilisi State University, Tbilisi, 1990)Google Scholar