The self-similar solutions to the mean curvature flow have been defined and studied on the Euclidean space. In this paper we propose a general treatment of the self-similar solutions to the mean curvature flow 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 results on special Lagrangian submanifolds on ℂn to the toric Calabi-Yau cones over Sasaki-Einstein manifolds.
|Number of pages||27|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2014 Oct 1|
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