Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on toric Calabi--Yau cones
Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on toric Calabi--Yau cones
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DOI：
10.18910/50982
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发表时间：
2011-12
影响因子：
0.4
通讯作者：
A. Futaki;Kota Hattori;Hikaru Yamamoto
中科院分区：
文献类型：
--
作者：
A. Futaki;Kota Hattori;Hikaru Yamamoto
在欧氏空间中定义并研究了平均曲率流的自相似解。本文给出了黎曼锥流形上平均曲率流自相似解的一般处理方法。作为一个典型的结果，我们推广了Huisken关于平均曲率流奇点的渐近行为的著名结果。我们还将关于$\mathbb C^n$上特殊拉格朗日子流形的结果推广到Sasaki-Einstein流形上的环面Calabi-Yau锥上。
The self-similar solutions to the mean curvature flows have been defined and studied on the Euclidean space. In this paper we initiate a general treatment of the self-similar solutions to the mean curvature flows on Riemannian cone manifolds. As a typical result we extend the well-known result of Huisken about the asymptotic behavior for the singularities of the mean curvature flows. We also extend the results on special Lagrangian submanifolds on $\mathbb C^n$ to the toric Calabi-Yau cones over Sasaki-Einstein manifolds.