| Gradient Flow of the Lβ-Functional |
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| 作者姓名： | Xiaoli Han Jiayu Li Jun Sun |
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| 作者单位： | Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China;School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026 AMSS CAS,Beijing 100190,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China;Hubei Key Laboratory of Computational Science,Wuhan University,Wuhan 430072,China |
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| 基金项目： | The research was supported by the National Natural Science Foundation of China,Nos.11721101,12071352,12031017 |
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| 摘 要： | In this paper,we start to study the gradient flow of the functional Lβ introduced by Han-Li-Sun in8].As a first step,we show that if the initial surface is symplectic in a K?hler surface,then the symplectic property is preserved along the gradient flow.Then we show that the singularity of the flow is characterized by the maximal norm of the second fundamental form.When β=1,we derive a monotonicity formula for the flow.As applications,we show that the l-tangent cone of the flow consists of the finite flat planes.
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| 关 键 词： | β-symplectic critical surfaces gradient flow monotonicity formula tangent cone |
Gradient Flow of the Lβ-Functional |
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| Xiaoli Han,Jiayu Li,Jun Sun.Gradient Flow of the Lβ-Functional[J].Communications in Mathematical Research,2021,37(1):113-140. |
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| Authors: | Xiaoli Han Jiayu Li Jun Sun |
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| Abstract: | In this paper,we start to study the gradient flow of the functional Lp introduced by Han-Li-Sun in8].As a first step,we show that if the initial surface is symplectic in a Kahler surface,then the symplectic property is pre-served along the gradient flow.Then we show that the singularity of the flow is characterized by the maximal norm of the second fundamental form.Whenβ= 1,we derive a monotonicity formula for the flow.As applications,we show that the A-tangent cone of the flow consists of the finite flat planes. |
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| Keywords: | β-symplectic critical surfaces gradient flow monotonicity formula tangent cone |
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