TY - JOUR
T1 - Gradient Flow of the $L_β$-Functional
AU - Han , Xiaoli
AU - Li , Jiayu
AU - Sun , Jun
JO - Communications in Mathematical Research 
VL - 1
SP - 113
EP - 140
PY - 2021
DA - 2021/02
SN - 37
DO - http://doi.org/10.4208/cmr.2020-0037
UR - https://global-sci.org/intro/article_detail/cmr/18627.html
KW - $β$-symplectic critical surfaces, gradient flow, monotonicity formula, tangent
cone.
AB - <p style="text-align: justify;">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.</p>