%0 Journal Article
%T Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on toric Calabi-Yau cones
%A Akito Futaki
%A Kota Hattori
%A Hikaru Yamamoto
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1112.5933v3