标题： 黎曼曲面上的散射理论 II：散射矩阵与广义周期映射 显示英文标题

标题： Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings

摘要： 我们为黎曼曲面上的调和1-形式构建了一种散射理论，该理论来源于涉及曲线系统和跳跃问题的边值问题。 我们以所谓的Schiffer算子的形式给出了散射矩阵的显式表达式，并证明了该矩阵是酉的。 我们还建立了正极化拉格朗日空间与带边黎曼曲面之间的一般联系，这统一了代数几何中紧致曲面的经典极化与普遍Teichmüller空间的无限维周期映射。 显示英文摘要

摘要： We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of integral operators which we call Schiffer operators, and show that the matrix is unitary. We also obtain a general association of positive polarizing Lagrangian spaces to bordered Riemann surfaces, which unifies the classical polarizations for compact surfaces of algebraic geometry with the infinite-dimensional period map of the universal Teichm\"uller space.