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| Mean Curvature Flow via Convex Functions on Grassmannian Manifolds |
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Citation： |
Yuanlong XIN,Ling YANG.Mean Curvature Flow via Convex Functions on Grassmannian Manifolds[J].Chinese Annals of Mathematics B,2010,31(3):315~328 |
| Page view： 1911
Net amount： 1538 |
Authors： |
Yuanlong XIN; Ling YANG; |
Foundation： |
the National Natural Science Foundation of China and the Science Foundation of
the Ministry of Education of China. |
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| Abstract： |
Using the convex functions on Grassmannian manifolds, the authors obtain the
interior estimates for the mean curvature flow of higher codimension. Confinable properties
of Gauss images under the mean curvature flow have been obtained, which reveal that if
the Gauss image of the initial submanifold is contained in a certain sublevel set of the
v-function, then all the Gauss images of the submanifolds under the mean curvature flow
are also contained in the same sublevel set of the v-function. Under such restrictions,
curvature estimates in terms of v-function composed with the Gauss map can be carried
out. |
Keywords： |
Mean curvature flow, Convex function, Gauss map |
Classification： |
53C44 |
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