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Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces

Miran Cerne
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Abstract

Let S be a bordered Riemann surface with genus g and m boundary components. For a smooth family of smooth Jordan curves in the complex plane parametrized by the boundary of S and such that all curves contain 0 in their interior we show that there exists a holomorphic solution of the corresponding Riemann-Hilbert problem with at most 2g+m-1 zeros on S.

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Miran Cerne. 2002-09-24. Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces. https://arxiv.org/abs/math/0209320

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