Singularity of mean curvature flow of Lagrangian submanifolds
نویسندگان
چکیده
منابع مشابه
Singularity of Mean Curvature Flow of Lagrangian Submanifolds
In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold Σ0 is Lagrangian and almost calibrated by ReΩ in a Calabi-Yau n-fold (M,Ω), and T > 0 is the first blow-up time of the mean curvature flow, then the tangent cone of the mean curvature flow at a singular point (X0, T ) is a stationary Lagrangian integer mul...
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It was proved that a blow-up solution to the mean curvature flow with positive mean curvature is an ancient convex solution, that is a convex solution which exists for time t from −∞. In this paper we study the geometry of ancient convex solutions. Our main results are contained in Theorems 1-3 below. Theorem 1 asserts that after normalization, the solution converges to a sphere or cylinder as ...
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A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite ...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 2004
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-003-0332-5