Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces
نویسندگان
چکیده
منابع مشابه
Nonlinear Riemann-hilbert Problem for Bordered Riemann Surfaces
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 C 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.
متن کاملSecond-order Functional-difference Equations. I: Method of the Riemann–hilbert Problem on Riemann Surfaces
An analytical method for scalar second-order functional-difference equations with meromorphic periodic coefficients is proposed. The technique involves reformulating the equation as a vector functional-difference equation of the first order and reducing it to a scalar Riemann–Hilbert problem for two finite segments on a hyperelliptic surface. The final step of the procedure is solution of the c...
متن کاملA Riemann-Hilbert problem for biorthogonal polynomials
We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin, Kapaev, and Bertola et al. We believe that our formulation may be tractable to asymptotic analysis.
متن کاملThe Riemann - Hilbert Problem for Holonomic Systems
The purpose of this paper is to give a proof to the equivalence of the derived category of holonomic systems and that of constructible sheaves. Let X be a paracompact complex manifold and let ® x and 0 x be the sheaf of differential operators and holomorphic functions, respectively. We denote by Mod(^z) the abelian category of left ^^-Modules and by D(^) its derived category. Let ~D^(^x) denote...
متن کاملCurves , Riemann - Hilbert Problem and Schlesinger Equations
We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices. Our approach is based on the finite gap integration method applied to study the Riemann-Hilbert by Kitaev and Korotkin [1], Deift, Its, Kapaev and Zhou [2] and Korotkin, [3]. This permits us to solve the Riemann-Hilbert prob...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2004
ISSN: 1080-6377
DOI: 10.1353/ajm.2004.0002