Gradient flow for -symplectic critical surfaces

  • Xiaoli Han

    Tsinghua University, Beijing, China
  • Jiayu Li

    University of Science and Technology of China, Hefei, China
  • Jun Sun

    Wuhan University, China
Gradient flow for $\beta$-symplectic critical surfaces cover

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In this paper we consider a gradient flow for the -functional introduced by the authors in Han–Li–Sun (2018). We first prove that the “symplectic” property is preserved along the gradient flow. Then we prove a monotonicity formula and an -regularity theorem for the flow. As consequences, we show that the -tangent cone of the flow consists of finite flat planes. Another application is that we can show that the flow exists globally and converges to a holomorphic curve if the initial surface is sufficiently close to a holomorphic curve and the ambient Käher–Einstein surface has positive scalar curvature.

Cite this article

Xiaoli Han, Jiayu Li, Jun Sun, Gradient flow for -symplectic critical surfaces. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2023), published online first

DOI 10.4171/AIHPC/100