The study on the deformation space of periodic minimal surfaces and its applications
| Project/Area Number |
15K04859
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Meijo University |
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Principal Investigator |
Ejiri Norio 名城大学, 理工学部, 教授 (80145656)
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| Project Period (FY) |
2015-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | Riemann surface / minimal surface / flat torus / Morse index / signature / CMC安定 / H amily / tP,tD family / rPD family / triply periodic surface / 相転移 / Jacobi operator / index / nullity / special geometry / deformation space / period map / limit / hyperelliptic / triply periodic / limit of minimal surface / Weierstrass data space |
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| Outline of Final Research Achievements |
In our world, soap bubbles are round. The proof is given by Mathematics. Thus, shapes except sphere do not appear. In a 3 dimensional flat torus(2 dimensional flat torus may be the face of a doughnut), what is the shape of soap bubbles? In 1992, Ross proved that Shoen's Gyroid, Schwarz' P surface and D surface are soap bubbles. We proved that H surface is a soap bubble and Schwarz'P surface is transformed into D surface under the deformation of the 3 dimensional flat torus containing P surface.
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| Academic Significance and Societal Importance of the Research Achievements |
n次元平坦トーラスの種数gの極小曲面面のMorse indexを求めるために変形空間にspecial pseudo Kaehler structure with signature (p,q)を導き、 q とMorse indexとの不等式とMorse indexを求めるalgorithmを与た。結果としてたくさんの極小曲面のMorse index が求められ応用として３次元平坦トーラスのシャボン玉の多様性がわかったことです。
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Report
(7 results)
Research Products
(8 results)
