2015 Fiscal Year Final Research Report
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 |
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| Research Field |
Geometry
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| Research Institution | Saga University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 幾何学 |
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| 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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| Free Research Field |
微分幾何学
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