GEOMETRY OF COMPLETE HYPERSURFACES EVOLVED BY MEAN CURVATURE FLOW 被引量：2

GEOMETRY OF COMPLETE HYPERSURFACES EVOLVED BY MEAN CURVATURE FLOW

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摘要 Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.

作者 SHENG WEIMIN

机构地区 Department of Mathematics

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第1期123-132,共10页 数学年刊（B辑英文版）

基金 Project supported by the National Natrual Science Foundation of China (No.10271106) the Natrual Science Foundation of Zhejiang Province, China (No.102033).

关键词 Mean curvature flow Maximum principle Complete hypersurfaces 完全超曲面平均曲率流几何奇异性不动点最大值原理流形完全解可变距离导数估计渐进体积率

分类号 O186.16 [理学—基础数学] O175.2 [理学—基础数学]

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参考文献18

1Cao, H. D. & Chow, B., Recent developments on the Ricci flow, Bull. Amer. Math. Soc., 36(1999),59-74.
2Cheeger, J. & Ebin, D., Comparison theorems in Riemannian geometry, North-Holland Publishing Company, Amsterdan, 1975.
3Ecker, K. & Huisken,G., Interior estimates for hypersurfaces moving by mean curvature, Invent, Math.,105(1991), 547-569.
4Hamilton, R. S., Three-manifolds with positive Ricci curvature, J. Differential Geom., 17(1982), 255-306.
5Hamilton, R. S., Four-manifolds with positive curvature operator, J. Differential Geom., 24(1986), 153-179.
6Hamilton,R. S., The Harnack estimate for the Ricci flow, J. Differential Geom., 37(1993), 225-243.
7Hamilton, R. S., Formation of singularities in the Ricci flow, Surveys in Differential Geom., 2(1995),7-136, International Press, Boston.
8Hamilton, R. S., Harnack estimate for the mean curvature flow, J. Differential Geom., 41(1995), 215-226.
9Hamilton, R. S., A compactness property for solutions of the Ricci flow, Amer. J. Math., 117(1995),545-572.
10Hamilton, R. S., Four manifolds with positive isotropic curvature, Comm. Anal. Geom., 5(1997), 1-92.

引证文献2

1Jie WANG.Harnack estimate for the H^k-flow[J].Science China Mathematics,2007,50(11):1642-1650. 被引量：1
2王捷.H^k流的微分Harnack估计[J].中国科学（A辑）,2007,37(10):1207-1214.

二级引证文献1

1Weimin SHENG Chao WU.On Asymptotic Behavior for Singularities of the Powers of Mean Curvature Flow[J].Chinese Annals of Mathematics,Series B,2009,30(1):51-66.

1YANG Liuqing.Nonexistence of Blow-Up Flows for Symplectic and Lagrangian Mean Curvature Flows[J].Journal of Partial Differential Equations,2012,25(3):199-207.
2Xinrong JIANG,Caisheng LIAO.On the Conditions of Extending Mean Curvature Flow[J].Chinese Annals of Mathematics,Series B,2012,33(1):61-72.
3Yi Bing SHEN,Xiao Hua ZHU.On Complete Hypersurfaces with Constant Mean Curvature and Finite L^p-norm Curvature in R^(n+1)[J].Acta Mathematica Sinica,English Series,2005,21(3):631-642.
4Jiayu LI,Liuqing YANG.Generalized Symplectic Mean Curvature Flows in Almost Einstein Surfaces[J].Chinese Annals of Mathematics,Series B,2014,35(1):33-50.
5Xiao Li HAN,Jun SUN.ε_0-Regularity for Mean Curvature Flow from Surface to Flat Riemannian Manifold[J].Acta Mathematica Sinica,English Series,2012,28(7):1475-1490. 被引量：1
6LiJiayu.MEAN CURVATURE FLOW OF GRAPHS IN ∑1×∑2[J].Journal of Partial Differential Equations,2003,16(3):255-265.
7蔡开仁.Mean curvature flow of hypersurfaces in Einsteinnian manifold[J].Chinese Science Bulletin,1996,41(7):616-616.
8Rongli HUANG.Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space[J].Chinese Annals of Mathematics,Series B,2011,32(2):187-200. 被引量：1
9WU Zhen(College of Mathematics and System Sciences, Shandong University, Ji’nan 250100, China).MAXIMUM PRINCIPLE FOR OPTIMAL CONTROLPROBLEM OF FULLY COUPLEDFORWARD-BACKWARD STOCHASTIC SYSTEMS[J].Systems Science and Mathematical Sciences,1998,11(3):249-259. 被引量：23
10沈一兵.ON CURVATURE PINCHING FOR MINIMAL AND KAEHLER SUBMANIFOLDS WITH ISOTROPIC SECOND FUNDAMENTAL FORM[J].Chinese Annals of Mathematics,Series B,1991,12(4):454-463. 被引量：1

Chinese Annals of Mathematics,Series B

2003年第1期

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GEOMETRY OF COMPLETE HYPERSURFACES EVOLVED BY MEAN CURVATURE FLOW 被引量：2

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