Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on Toric Calabi-Yau cones

Akito Futaki, Kota Hattori, Hikaru Yamamoto

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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.

Original languageEnglish
Pages (from-to)1053-1079
Number of pages27
JournalOsaka Journal of Mathematics
Issue number4
Publication statusPublished - 2014 Oct 1


ASJC Scopus subject areas

  • Mathematics(all)

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