L29A
檢討期末考
這裡U代表複平面上的單位開圓盤
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, Ω≠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.
0:00 第1題
5:56 第2題
10:35 第3題
14:08 第4題
28:33 第5題
33:27 第6,7題