Study of the moduli theory of periodic minimal surfaces in terms of differential geometry
Project/Area Number |
24740047
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Geometry
|
Research Institution | Saga University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 幾何学 / 周期的極小曲面 / Morse指数 / 退化次数 / 面積最小 / 極小曲面 / モジュライ理論 / 国際情報交換 |
Outline of Final Research Achievements |
We would study periodic minimal surfaces in the Euclidean space in terms of the differential geometry. In particular, we treated Morse indices of triply periodic minimal surfaces. In this period, we could succeed in computing many Morse indices for families of minimal surfaces which have been studied in physics and chemistry. Also, we could succeed in mathematical description of Lamellar structure by limits of triply perioddic minimal surfaces. Moreover, we obtained the existence and uniqueness results for a comlete minimal surface of finite total curvature in the Euclidean space.
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Report
(5 results)
Research Products
(20 results)