• Berger’s formulas and their applications in symplectic mean curvature flow

• # Fulltext

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

• # Keywords

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

• # Abstract

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.

• # Author Affiliations

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

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019