2015 Fiscal Year Final Research Report
Challenging study on self-shrinkers of mean curvature flow and applications
| Project/Area Number |
25610016
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Fukuoka University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 平均曲率フロー / 最大値原理 / 部分多様体 / セルフ-シュリンカー / 面積汎関数の変分 |
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| Outline of Final Research Achievements |
We generalize the maximum principle due to Omori and Yau for Laplacian to L operator on complete self-shrinkers of mean curvature flow. Making use of this generalized maximum principle for L operator, we study complete self-shrinkers of mean curvature and give a complete classification for 2-dimensional complete self-shrinkers in the 3-dimensional Euclidean space. Furthermore, for complete self-shrinkers of mean curvature flow with polynomial area growth, we get the second pinching constant of the constant length of the second fundamental form. We also prove a universal inequality on eigenvalues of L operator in complete self-shrinkers. According to this universal inequality, we obtain an upper bound and a lower bound of eigenvalues for L operator in complete self-shrinkers.
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| Free Research Field |
幾何学
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