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| THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS |
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Citation： |
Liu Taishun,Ren Guangbin.THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS[J].Chinese Annals of Mathematics B,1998,19(4):401~408 |
| Page view： 1439
Net amount： 1108 |
Authors： |
Liu Taishun; Ren Guangbin |
Foundation： |
the National Natural Science Foundation of China and the National Education Committee Doctoral Foundation |
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| Abstract： |
The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains. This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it.
In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables. |
Keywords： |
Starlike mappings, Growth theorem,
Starlike circular domains |
Classification： |
32A30, 30C25 |
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