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Two-dimensional graphs moving by mean curvature flow
Chen, JY; Li, JY; Tian, G
2002-04-01
Source PublicationACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN1439-8516
Volume18Issue:2Pages:209-224
AbstractA surface Sigma is a graph in R-4 if there is a unit constant 2-form w on R 4 such that (e(1) boolean AND e(2), w) greater than or equal to v(0) > 0 where (e(1), e(2)) is an orthonormal frame on Sigma. We prove that, if v(0) greater than or equal to 1/root2 on the initial surface, then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution. A surface Sigma is a graph in M-1 x M-2 where M-1 and M-2 are Riemann surfaces, if (e(1) boolean AND e(2), w(1)) greater than or equal to v(0) > 0 where w(1) is a Kahler form on M-1. We prove that, if M is a Kahler-Einstein surface with scalar curvature R, v(0) greater than or equal to 1/root2 on the initial surface, then the mean curvature flow has a global solution and it sub-converges to a minimal surface, if, in addition, R greater than or equal to 0 it converges to a totally geodesic surface which is holomorphic.
KeywordMean curvature flow 2-dimensional graphs in R-4 Self-similar solution
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000175594200001
PublisherSPRINGER-VERLAG BERLIN
Citation statistics
Cited Times:24[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/17128
Collection中国科学院数学与系统科学研究院
Affiliation1.Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
2.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
3.Fudan Univ, Dept Math, Shanghai 200433, Peoples R China
4.MIT, Dept Math, Cambridge, MA 02139 USA
Recommended Citation
GB/T 7714
Chen, JY,Li, JY,Tian, G. Two-dimensional graphs moving by mean curvature flow[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2002,18(2):209-224.
APA Chen, JY,Li, JY,&Tian, G.(2002).Two-dimensional graphs moving by mean curvature flow.ACTA MATHEMATICA SINICA-ENGLISH SERIES,18(2),209-224.
MLA Chen, JY,et al."Two-dimensional graphs moving by mean curvature flow".ACTA MATHEMATICA SINICA-ENGLISH SERIES 18.2(2002):209-224.
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