Click here to view fulltext PDF

Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/130/0029

Symplectic mean curvature flow; holomorphic curve; positive holomorphic sectional curvature

In this paper, we recall some well known Berger’s formulas. As their applications, we prove that if the local holomorphic pinching constant is $\gamma$ < 2, then there exists a positive constant $\delta$ > $\frac{29(\lambda−1)} {\sqrt{(48−24\lambda)^{2}+(29\lambda−29)^{2}}}$ such that cos $\alpha \geq \delta$ is preserved along the mean curvature flow, improving Li–Yang’s main theorem in Li and Yang (Geom. Dedicata 170 (2014) 63–69). We also prove that when cos $\alpha$ is close enough to 1, then the symplectic mean curvature flow exists globally and converges to a holomorphic curve.

SHIJIN ZHANG¹

1. School of Mathematical Sciences, Beihang University, Beijing 100191, People’s Republic of China

Published

15 March 2020

Manuscript received

7 August 2018

Manuscript revised

23 December 2018

Accepted

30 September 2019

Early published

Unedited version published online

Final version published online

19 March 2020