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Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 126, Number 1, February 2004
- pp. 65-87
- 10.1353/ajm.2004.0002
- Article
- Additional Information
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Let Σ be a bordered Riemann surface with genus g and m boundary components. Let {γz}z∈∂Σ be a smooth family of smooth Jordan curves in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] which all contain the point 0 in their interior. Then there exists a holomorphic function f(z) on Σ smooth up to the boundary with at most 2g + m - 1 zeros on Σ such that f(z) ∈ γz for every z ∈ ∂Σ.