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

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 Huisk...

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Veröffentlicht in:	Osaka journal of mathematics 2014-10, Vol.51 (no. 4), p.1053-1081
Hauptverfasser:	Futaki, Akito, Hattori, Kota, Yamamoto, Hikaru
Format:	Artikel
Sprache:	eng
Schlagworte:	53C21 53C55 55N91
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creator	Futaki, Akito Hattori, Kota Yamamoto, Hikaru
description	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 \mathbb{C}^{n} to the toric Calabi--Yau cones over Sasaki--Einstein manifolds.
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subjects	53C21 53C55 55N91
title	Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on toric Calabi--Yau cones
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