Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If $U$ is a polydisc in $\mathbb C^n$, that is, $U=\{z \in \mathbb C^n:|z_i|<1\}$, can we find a biholomorphic map from $U$ to $\mathbb C^n$?

share|improve this question
2  
Your edit completely changed the question... :-/ –  Mariano Suárez-Alvarez Feb 15 '13 at 22:16
1  
The best would be for you to undo that edit and ask a separate question. –  Mariano Suárez-Alvarez Feb 15 '13 at 22:17

2 Answers 2

up vote 2 down vote accepted

In an open set biholomorphic to $\mathbb C^n$ there are no bounded holomorphic functions which are not constant.

share|improve this answer

In the case $n = 1$, the unit disc is not biholomophic to $\mathbb C$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.