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A mean-curvature flow along a Kahler-Ricci flow
Han, Xiaoli1; Li, Jiayu2,3; Zhao, Liang4
2018
Source PublicationINTERNATIONAL JOURNAL OF MATHEMATICS
ISSN0129-167X
Volume29Issue:1Pages:25
AbstractLet (M, (g) over bar) be a Kahler surface, and S an immersed surface in M. The Kahler angle of S inM is introduced by Chern andWolfson [Am. J. Math. 105 (1983) 59-83]. Let (M, (g) over bar (t)) evolve along the Kahler- Ricci flow, and Sigma t in (M, (g) over bar (t)) evolve along the mean- curvature flow. We show that the Kahler angle alpha(t) satisfies the evolution equation (partial derivative/partial derivative(t) - Delta) cos alpha = |(del) over bar J Sigma(t)|(2) cos alpha +Rsin(2) alpha cos alpha, where R is the scalar curvature of (M, (g) over bar (t)). The equation implies that if the initial surface is symplectic (Lagrangian), then, along the flow, St is always symplectic (Lagrangian) at each time t, which we call a symplectic (Lagrangian) Kahler-Ricci mean-curvature flow. In this paper, we mainly study the symplectic Kahler-Ricci mean-curvature flow.
KeywordKahler angle Kahler-Ricci flow mean-curvature flow symplectic surface
DOI10.1142/S0129167X18500064
Language英语
Funding ProjectNSF in China[11131007] ; NSF in China[11471014] ; NSF in China[11201028]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000423846000006
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29443
Collection数学所
Affiliation1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
2.Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China
3.AMSS CAS, Beijing 100190, Peoples R China
4.Beijing Normal Univ, MOE, LMCS, Sch Math Sci, Beijing 100875, Peoples R China
Recommended Citation
GB/T 7714
Han, Xiaoli,Li, Jiayu,Zhao, Liang. A mean-curvature flow along a Kahler-Ricci flow[J]. INTERNATIONAL JOURNAL OF MATHEMATICS,2018,29(1):25.
APA Han, Xiaoli,Li, Jiayu,&Zhao, Liang.(2018).A mean-curvature flow along a Kahler-Ricci flow.INTERNATIONAL JOURNAL OF MATHEMATICS,29(1),25.
MLA Han, Xiaoli,et al."A mean-curvature flow along a Kahler-Ricci flow".INTERNATIONAL JOURNAL OF MATHEMATICS 29.1(2018):25.
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