Research on Schottky groups and Schottky spaces
| Project/Area Number |
10640158
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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 | Shizuoka University |
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Principal Investigator |
SATO Hiroki Shizuoka University, Science, Professor, 理学部, 教授 (40022222)
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| Co-Investigator(Kenkyū-buntansha) |
AKUTAGAWA Kazuo Shizuoka University, Science, Associate Professor, 理学部, 助教授 (80192920)
NAKANISHI Toshihiro Nagoya University, Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (00172354)
OKUMURA Yoshihide Shizuoka University, Science, Associate Professor, 理学部, 助教授 (90214080)
KUMURA Hironori Shizuoka University, Science, Assistant Professor, 理学部, 助手 (30283336)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1998: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | Schottky group / Schottky space / Jorgensen group / Jorgensen's inequality / Kleinian group / Teichmuller space / hyperbolic space / Hausdorff dimension / シヨツトキイ群 / シヨツトキイ空間 / 調和写像 |
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| Research Abstract |
We have studied the following three themes from 1998 to 1999.
1. Classical Schottky space of real type.
2. Jorgensen numbers.
3. Jorgensen groups.
1. Classical Schottky space of real type. We classified the classical Schottky space of real type of genus two into eight types. We represented the shape of their spaces and found generators for the Schottky modular groups acting on the above spaces. Furthermore we determine fundamental regions for the Schottky modular groups.
2. Jorgensen numbers. We found the best lower bounds for all kinds of the classical Schottky spaces of real type considered in 1. We submited these results to J. Math. Soc. Japan.
3. Jorgensen groups. A Jorgensen group is a non-elementary discrete group whose Jorgensen number is one. In 1998 we considered two one-parameter families of Jorgensen groups. We talked about these results at State University of New York at Stony Brook, Rutgers University at Newark and at New Brunswick in 1998. The results has been printed in Contemporary Mathematics (the proceeding of The Second Ahlfors-Bers Colloquium) in February, 2000. In 1999 we considered distribution of Jorgensen groups on the fiber over the unit circle. In particular, we studied new two one-paramter families of Jorgensen groups on it. We talked about the results at the international conference (ISAAC) in August, 1999. We invited Professor I. Kra at State University of New York at Stony Brook to talk about Schottky groups and the Schottky space in January, 2000. We are preparing to submit some results obtained between April, 1999 and February, 2000.
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Report
(3 results)
Research Products
(24 results)
