程守慶教授-複變數函數論作業專區

见

https://ocw.nthu.edu.tw/ocw/index.php?page=course_news_content&cid=289&id=1014

期末考试题及讲解见下面视频合集的最后一P

第1題: Let Ω=C\{z| |z|≤1}. Characterize Aut(Ω).

第2題: Does there exist a holomorphic function from U onto C?

第3題: Let Ω be a simply-connected domain in C, . Show that there exists a bounded one-to-one holomorphic function on Ω.

第4題: Find a biholomorphic mapping from the domain Ω onto the open unit disc. See 15:30.

第5題: Find a biholomorphic mapping from the domain Ω bounded by two circles to the annulus A={z| a<|z|<1}. Also find a. See 28:55.

第6題: State and prove Vitali's theorem.

第7題: State and prove Poincaré's inequivalence theorem.