منابع مشابه
Gauss Maps of the Mean Curvature Flow
Let F : Σ n × [0, T) → R n+m be a family of compact immersed submanifolds moving by their mean curvature vectors. We show the Gauss maps γ : (Σ n , g t) → G(n, m) form a harmonic heat flow with respect to the time-dependent induced metric g t. This provides a more systematic approach to investigating higher codimension mean curvature flows. A direct consequence is any convex function on G(n, m)...
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We study the mean curvature flow of complete space-like submanifolds in pseudo-Euclidean space with bounded Gauss image, as well as that of complete submanifolds in Euclidean space with convex Gauss image. By using the confinable property of the Gauss image under the mean curvature flow we prove the long time existence results in both cases. We also study the asymptotic behavior of these soluti...
متن کاملSe p 20 02 Gauss Maps of the Mean Curvature Flow
Let F : Σ n × [0, T) → R n+m be a family of compact immersed sub-manifolds moving by their mean curvature vector. We show the Gauss maps γ : (Σ n , g t) → G(n, m) form a harmonic heat flow with respect to the time-dependent induced metric g t. This provides a more systematic approach to investigate higher codimension mean curvature flows. A direct consequence is any convex function on G(n, m) p...
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Given a Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: eg, finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for example, proves that the minimal Lagrangian orbits are isolated.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2003
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2003.v10.n3.a2