2012 Fiscal Year Final Research Report
A study on holomorphic mappings and harmonic mappings on the unit balls
| Project/Area Number |
22540213
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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, 准教授 (20241226)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 複素解析 |
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| Research Abstract |
We present a new geometric construction of Loewner chains in one and several complex variables which holds on complete hyperbolic complex manifolds, and as a consequence, we obtain a univalent solution for any Loewner partial differential equation. We proved that the Loewner variation of an extreme point (respectively a support point) is also an extreme point (respectively a support point). We proved the two-point distortion theorems for affine and linearly invariant family of harmonic functions on the unit disc or of pluriharmonic mappings on the Euclidean unit ball. We obtained upper bounds for the distortion and the growth of holomorphic linearly invariant families on homogeneous unit balls.
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