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 |
Research Field |
Geometry
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Research Institution | Fukuoka University |
Principal Investigator |
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Project Period (FY) |
2013-04-01 – 2016-03-31
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Project Status |
Completed (Fiscal Year 2015)
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Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / せルフ-シュリンカー / 部分多様体の幾何学 / 固有値理論 / 安定性作用素 |
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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Report
(4 results)
Research Products
(30 results)
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[Presentation] Complete self-shrinkers2016
Author(s)
Qing-Ming Cheng
Organizer
Seminar on Mathematics, Guangxi Normal University
Place of Presentation
Guangxi Normal University, China
Year and Date
2016-03-25
Related Report
Int'l Joint Research / Invited
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[Presentation] Geometry of λ-hypersurfaces2015
Author(s)
Qing-Ming Cheng
Organizer
International conference on geometry and topology of submanifolds
Place of Presentation
Henan Normal University, China
Year and Date
2015-09-25
Related Report
Int'l Joint Research / Invited
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