Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on symplectic mean curvature flows in K\"ahler surfaces with
  positive holomorphic sectional curvatures   In this paper, we mainly study the mean curvature flow in K\"ahler surfaces
with positive holomorphic sectional curvatures. First, we prove that if the
ratio $\lambda$ of the maximum and the minimum of the holomorphic sectional
curvatures $< 2$, 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 flow, improving the
main theorem in [LY]; Secondly, as similar as the main theorem in [HL0], we
prove that when $\cos\alpha$ is close to $1$ enough, then the symplectic mean
curvature flow exists for long time and converges to a holomorphic curve;
Finally, we prove that the symplectic mean curvature flow on K\"ahler surfaces
with $\lambda\leq 1+\frac{1}{200}$ exists for long time and converges to a
holomorphic curve if the initial surface satisfies a pinching condition, which
generalize one of the main theorems in [HLY].

14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg