Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces
复变函数
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0209320,
title = {Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces},
author = {Miran Cerne},
journal= {arXiv preprint arXiv:math/0209320},
year = {2007}
}
备注
18 pages