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 A mean-curvature flow along a Kahler-Ricci flow Han, Xiaoli1; Li, Jiayu2,3 ; Zhao, Liang4 2018 Source Publication INTERNATIONAL JOURNAL OF MATHEMATICS ISSN 0129-167X Volume 29Issue:1Pages:25 Abstract Let (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. Keyword Kahler angle Kahler-Ricci flow mean-curvature flow symplectic surface DOI 10.1142/S0129167X18500064 Language 英语 Funding Project NSF in China ; NSF in China ; NSF in China WOS Research Area Mathematics WOS Subject Mathematics WOS ID WOS:000423846000006 Publisher WORLD SCIENTIFIC PUBL CO PTE LTD Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/29443 Collection 数学所 Affiliation 1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China2.Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China3.AMSS CAS, Beijing 100190, Peoples R China4.Beijing Normal Univ, MOE, LMCS, Sch Math Sci, Beijing 100875, Peoples R China Recommended CitationGB/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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