2015 Fiscal Year Final Research Report
Studies on proper holomorphic mappings, univalent holomorphic mappings and harmonic mappings on the unit balls
| Project/Area Number |
25400151
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu Sangyo University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HONDA Tatsuhiro 広島工業大学, 工学部, 教授 (20241226)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | レブナー鎖 / 螺旋型写像 / ルンゲ領域 / シュワルツの補題 / シュワルツ・ピックの補題 / 多重調和写像 / 単葉正則写像 |
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| Outline of Final Research Achievements |
We introduce normalized Loewner chains in the unit ball, which we call ``spacious". We apply our construction to the study of support points, extreme points in the class S0 of univalent holomorphic mappings.
We generalize the harmonic Schwarz lemma to pluriharmonic mappings of the unit ball of a complex Banach space. We obtain a generalization of the harmonic Schwarz-Pick lemma to the case of pluriharmonic mappings of the bounded symmetric domain in a complex Banach space. We obtain the Landau and the Bloch theorems on bounded symmetric domains.
We showed that any spirallike domain is Runge. We also showed the local uniform approximation of biholomorphic mappings on a spirallike domain, by automorphisms of Cn. As an application of the above result, we showed that any Loewner PDE in a complete hyperbolic spirallike domain admits an essentially unique univalent solution.
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| Free Research Field |
多変数函数論
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