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

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume51
Issue number4
Publication statusPublished - 2014 Oct 1
Externally publishedYes

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Mean Curvature Flow
Calabi-Yau
Self-similar Solutions
Cone
Einstein Manifold
Lagrangian Submanifold
Euclidean space
Asymptotic Behavior
Singularity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on Toric Calabi-Yau cones. / Futaki, Akito; Hattori, Kota; Yamamoto, Hikaru.

In: Osaka Journal of Mathematics, Vol. 51, No. 4, 01.10.2014, p. 1053-1079.

Research output: Contribution to journalArticle

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