2011 Fiscal Year Final Research Report
Dynamics of curves and surfaces governed by various geometric evolution equations
| Project/Area Number |
21740110
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University (2011)
Iwate University (2009-2010) |
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Principal Investigator |
OKABE Shinya 東北大学, 大学院・理学研究科, 准教授 (70435973)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 偏微分方程式論 / 変分法 |
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| Research Abstract |
The summary of our results are stated as follows :(1)We prove that there exists a critical point of the variational problem for a certain space-time functional defined on planar curves which is concerned with stochastically perturbed mean curvature flow for curves ; (2)we show that, for a planar smooth non-closed curve with finite or infinite length, there exists a smooth solution of the steepest descent flow for the modified total squared curvature for any finite time. Moreover, we prove that, for an initial curve perturbed from line segment, the solution smoothly converges to a stationary solution along a certain sequence of time.
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