| 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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| 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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