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| Mean Curvature Flow of Arbitrary Codimension in Complex Projective Spaces* |
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Citation： |
Li LEI,Hongwei XU.Mean Curvature Flow of Arbitrary Codimension in Complex Projective Spaces*[J].Chinese Annals of Mathematics B,2023,44(6):857~892 |
| Page view： 1267
Net amount： 698 |
Authors： |
Li LEI; Hongwei XU |
Foundation： |
National Natural Science Foundation of China (Nos. 12071424,11531012, 12201087) |
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| Abstract： |
Recently, Pipoli and Sinestrari [Pipoli, G. and Sinestrari, C., Mean curvature flow of pinched submanifolds of CPn, Comm. Anal. Geom., 25, 2017, 799–846] initiated the study of convergence problem for the mean curvature flow of small codimension in the complex projective space CPm. The purpose of this paper is to develop the work due to Pipoli and Sinestrari, and verify a new convergence theorem for the mean curvature flow of arbitrary codimension in the complex projective space. Namely, the authors prove that if the initial submanifold in CPm satisfies a suitable pinching condition, then the mean curvature flow converges to a round point in finite time, or converges to a totally geodesic submanifold as t → ∞. Consequently, they obtain a differentiable sphere theorem for submanifolds in the complex projective space. |
Keywords： |
Mean curvature flow, Submanifolds of arbitrary codimension, Complex projective space, Convergence theorem, Differentiable sphere theorem |
Classification： |
53C44, 53C40, 53C20, 58J35 |
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