Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces
β Scribed by Cerne, Miran
- Book ID
- 118225401
- Publisher
- John Hopkins University Press
- Year
- 2004
- Tongue
- English
- Weight
- 446 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0002-9327
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π SIMILAR VOLUMES
We prove that the interior of any compact complex curve with smooth boundary in C 2 admits a proper holomorphic embedding into C 2 . In particular, if D is a bordered Riemann surface whose closure admits a holomorphic embedding into C 2 , then D admits a proper holomorphic embedding into C 2 .
## Abstract Nonlinear Riemann β Hilbert problems (RHP) generalize two fundamental classical problems for complex analytic functions, namely: 1. the conformal mapping problem, and 2. the linear Riemann β Hilbert problem. This paper presents new results on global existence for the nonlinear (RHP) in
We discuss a class of solutions to the Ernst equation (the stationary axisymmetric Einstein equations) obtained as solutions of a generalized scalar Riemann-Hilbert problem on a hyperelliptic Riemann surface. The singular structure of these solutions is studied for arbitrary genus of the Riemann sur