Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces
Copyright policy )Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces
Let Σ be a bordered Riemann surface with genus g and m boundary components. Let { γ z } 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 2 g + m - 1 zeros on Σ such that f ( z ) ∈ γ z for every z ∈ ∂Σ.
Riemann-Hilbert problem, Mathematics - Complex Variables, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, embedding into convex domains, 30E25, 35Q15 (Primary) 32E20 (Secondary), Riemann surfaces, bordered Riemann surfaces, embedding, FOS: Mathematics, Boundary value problems in the complex plane, Riemann-Hilbert problems in context of PDEs, Complex Variables (math.CV)
Riemann-Hilbert problem, Mathematics - Complex Variables, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, embedding into convex domains, 30E25, 35Q15 (Primary) 32E20 (Secondary), Riemann surfaces, bordered Riemann surfaces, embedding, FOS: Mathematics, Boundary value problems in the complex plane, Riemann-Hilbert problems in context of PDEs, Complex Variables (math.CV)
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