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| A NECESSARY AND SUFFICIENT CONDITION THAT BIHOLOMORPHIC MAPPINGS ARESTARLIKE ON A CLASS OF REINHARDT DOMAINS |
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Citation： |
Gong Sheng（龚升）,Wang Shikun（王世坤）,Yu Qihuang(余其煌).A NECESSARY AND SUFFICIENT CONDITION THAT BIHOLOMORPHIC MAPPINGS ARESTARLIKE ON A CLASS OF REINHARDT DOMAINS[J].Chinese Annals of Mathematics B,1992,13(1):95~104 |
| Page view： 906
Net amount： 743 |
Authors： |
Gong Sheng（龚升）; Wang Shikun（王世坤）;Yu Qihuang(余其煌) |
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| Abstract： |
This paper studies the Reinhardt domains B defined as
$B \equiv{Z=(\z_1,\z_2,\cdots,\z_n \in C^n|\[\sum\limits_{i = 1}^n {|{z_i}{|^{{p_i}}} < 1} \],2p_n>p_1\geq p_2\geq \cdots \geq p_n >1.}$
The Schwartz lemma for B is established. Using it the authors give a necessary aad sufficient condition that a local biholomorphic mapping from B to $C^n$ is starlike. It is reduced to the Suffridge's theorem in the case $p_1=p_2=\cdots=p_n>1$. |
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