高等亏格Riemann surfaces上的Ginzburg-Landau方程
Ginzburg-Landau equations on Riemann surfaces of higher genus
摘要：
本文研究了任意亏格Riemann曲面上的Ginzburg-Landau方程。特别是：- 我们明确地构建（局部模空间的规范等效）解决方案在附近的常曲率的; -分类全纯结构的线丛上产生的解决方案的方程的程度，阿贝尔-雅可比映射，对称产品的表面; -确定的形式的能量和确定当它低于能量的常曲率（正常）的解决方案。
英文摘要：
We study the Ginzburg-Landau equations on Riemann surfaces of arbitrary genus. In particular: - we construct explicitly the (local moduli space of gauge-equivalent) solutions in a neighbourhood of the constant curvature ones; - classify holomorphic structures on line bundles arising as solutions to the equations in terms of the degree, the Abel-Jacobi map, and symmetric products of the surface; - determine the form of the energy and identify when it is below the energy of the constant curvature (normal) solutions.
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