| Project/Area Number |
22340025
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Tohoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SHIGA Hiroshige 東京工業大学, 理工学研究科, 教授 (10154189)
YANAGIHARA Hiroshi 山口大学, 理工学研究科, 教授 (30200538)
SAKAN Ken-ichi 大阪市立大学, 理学研究科, 准教授 (70110856)
MATSUZAKI Katsuhiko 早稲田大学, 教育・総合科学学術院, 教授 (80222298)
FUJIKAWA Ege 千葉大学, 理学研究科, 准教授 (80433788)
阿部 誠 広島大学, 大学院・理学研究科, 教授 (90159442)
水田 弘 広島大学, 大学院・理学研究科, 教授 (00093815)
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| Co-Investigator(Renkei-kenkyūsha) |
MIZUTA Yoshihiro 広島工業大学, 工学部, 教授 (00093815)
TANIGUCHI Masahiko 奈良女子大学, 理学部, 教授 (50108974)
FUJIWARA Koji 京都大学, 理学研究科, 教授 (60229078)
ABE Makoto 広島大学, 理学研究科, 教授 (90159442)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥17,290,000 (Direct Cost: ¥13,300,000、Indirect Cost: ¥3,990,000)
Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Keywords | 等角写像 / 単葉函数 / 双曲計量 / 錐特異性 / シュワルツ微分 / 極値問題 / 擬等角写像 / 一様完全 / 面積不等式 / 幾何学的函数論 / 変動領域 / 単葉性判定法 / シュワルツ補題 / ベキ変形 / グルンスキー係数 / ベキ行列 / 退化ベルトラミ方程式 / 半円環 |
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| Outline of Final Research Achievements |
Geometric Function Theory deals with problems finding relations between geometrically described (simply-connected) domains in the plane and analytic properties of conformal mappings onto them. Bieberbach conjectured that, for a conformal mapping f(z)=a_0+a_1z+a_2z^2+... normalized by a_0=0, a_1=1, the modulus |a_n| of a_n is not greater than n.This conjecture was finally proved by de Branges in his 1985 paper. In the present research project, for example, we showed that the set of conformal mappings as above with half-integral coefficients consists of exactly 21 functions. The similar set for the integral coefficients was previously known to consist of 9 functions.
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