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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6789
標題: | 均曲率流的拉格拉奇自同構解 Lagrangian Self-Similar Solutions for Mean Curvature Flow |
作者: | Yang-Kai Lue 呂楊凱 |
指導教授: | 李瑩英(Yng-Ing Lee) |
關鍵字: | 拉格拉奇,同構解,均曲率, Self-Similar solution,Lagrangian,mean curvature vector, |
出版年 : | 2012 |
學位: | 博士 |
摘要: | In this thesis, we generalize Colding and
Minicozzi's work on the stability of self-shrinkers in the hypersurface case to higher co-dimensional cases. The 1st and 2nd variation formulae of the $F$-functional are derived and an equivalent condition to the stability in general codimension is found. Using the equivalent condition, we can classify $F$-stable product self-shrinkers and show that the Lagrangian self-shrinkers given by Anciaux are $F$- unstable. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6789 |
全文授權: | 同意授權(全球公開) |
顯示於系所單位: | 數學系 |
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ntu-101-1.pdf | 422.31 kB | Adobe PDF | 檢視/開啟 |
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