Complex Analysis

  • 紧黎曼曲面上的曲线本质上是代数曲线
  • 由整个复平面到圆盘的共形映射是不存在的,但是总有从一个连通的非平凡开集到圆盘的共形映射

the Riemann mapping theorem guarantees the existence of a conformal map from any proper, simply open set to the disc, or equivalently to the upper half plane.

week 8

week 7

week 6

week 5

week 4

week 3

sorry week 1 and 2 are temporarily lost!