Year: 2021
Author: Xiaoli Han, Jiayu Li, Jun Sun
Communications in Mathematical Research , Vol. 37 (2021), Iss. 1 : pp. 113–140
Abstract
In this paper, we start to study the gradient flow of the functional $L_β$ introduced by Han-Li-Sun in [8]. As a first step, we show that if the initial surface is symplectic in a Kähler 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 $λ$-tangent cone of the flow consists of the finite flat planes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0037
Communications in Mathematical Research , Vol. 37 (2021), Iss. 1 : pp. 113–140
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: $β$-symplectic critical surfaces gradient flow monotonicity formula tangent cone.