黎曼曲面上的散射理论 II：散射矩阵与广义周期映射
微分几何
2025-06-11 v1 代数几何
复变函数
摘要
我们构建了黎曼曲面上调和 1-形式的散射理论，该理论源自涉及曲线系统和跳跃问题的边值问题。我们获得了散射矩阵用积分算子表示的显式表达式，我们称这些算子为 Schiffer 算子，并证明了该矩阵是幺正的。我们还得到了正极化拉格朗日空间与带边黎曼曲面的一般关联，该关联将代数几何中紧致曲面的经典极化与万有 Teichm\"uller 空间的无穷维周期映射统一起来。
关键词
引用
@article{arxiv.2506.08166,
title = {Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings},
author = {Eric Schippers and Wolfgang Staubach},
journal= {arXiv preprint arXiv:2506.08166},
year = {2025}
}
备注
The paper "A scattering theory of harmonic one-forms on Riemann surfaces" [arXiv:2112.00835] was divided into four parts. This is part 4 in that division which has been revised and made self-contained