Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hermitian metrics with negative mean curvature on holomorphic vector
  bundles   In this paper, we study holomorphic vector bundles over compact Gauduchon
manifolds. Using the continuity method, we prove the existence of
$L^{p}$-approximate critical Hermitian structure. As its application, we show
that a holomorphic vector bundle admits a Hermitian metric with negative mean
curvature if and only if the maximum of slopes of all of its subsheaves is
negative. Furthermore, we study the limiting behavior of the
Hermitian-Yang-Mills flow. We prove the minimum of the smallest eigenvalue of
the mean curvature is increasing along the Hermitian-Yang-Mills flow, while the
maximum of the biggest eigenvalue is decreasing; we show that they converge to
certain geometric invariants. Finally, we give some applications.

5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph