Gradient Flow of the Lβ-Functional

• 来源期刊: 数学研究通讯
• 年，卷（期）: 2021,（1）
• 页码范围: 113-140
• 页数: 28页
• 语种: 英文
• DOI: 10.4208/cmr.2020-0037

摘要

In this paper,we start to study the gradient flow of the functional Lp introduced by Han-Li-Sun in[8].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.