Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of approximate Hermitian-Einstein structures on semi-stable
  bundles   The purpose of this paper is to investigate canonical metrics on a
semi-stable vector bundle E over a compact Kahler manifold X. It is shown that,
if E is semi-stable, then Donaldson's functional is bounded from below. This
implies that E admits an approximate Hermitian-Einstein structure, generalizing
a classic result of Kobayashi for projective manifolds to the Kahler case. As
an application some basic properties of semi-stable vector bundles over compact
Kahler manifolds are established, such as the fact that semi-stability is
preserved under tensor product and certain exterior and symmetric products.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
18
The categories of this paper are: econ
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio