Questions in category: 黎曼曲面 (Riemann Surface)

## 1. 全纯函数的几种等价定义

Posted by haifeng on 2019-11-03 19:42:31 last update 2020-12-06 10:12:44 | Answers (1) | 收藏

$\lim_{z\rightarrow z_0}\frac{f(z)-f(z_0)}{z-z_0}$

$\begin{cases} u_x=v_y,\\ u_y=-v_x. \end{cases}$

$f(z)$ 在 $z_0$ 全纯也等价于

$\frac{\partial f}{\partial\bar{z}}\biggr|_{z=z_0}=0$.

\begin{aligned} \frac{\partial}{\partial z}=\frac{1}{2}(\frac{\partial}{\partial x}-i\frac{\partial}{\partial y}),\\ \frac{\partial}{\partial\bar{z}}=\frac{1}{2}(\frac{\partial}{\partial x}+i\frac{\partial}{\partial y}). \end{aligned}

Remark:

References:

## 2. 黎曼球面上的亚纯函数必为有理函数.

Posted by haifeng on 2012-08-08 06:04:14 last update 2012-08-08 06:04:14 | Answers (0) | 收藏
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