Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler
  manifolds   We study the Yang-Mills flow on a holomorphic vector bundle E over a compact
Kahler manifold X . Along a solution of the flow, we show the curvature
$i\Lambda F(A_t)$ approaches in $L^2$ an endomorphism with constant eigenvalues
given by the slopes of the quotients from the Harder-Narasimhan filtration of
E. This proves a sharp lower bound for the Hermitian-Yang-Mills functional and
thus the Yang-Mills functional, generalizing to arbitrary dimension a formula
of Atiyah and Bott first proven on Riemann surfaces. Furthermore, we show any
reflexive extension to all of X of the limiting bundle $E_\infty$ is isomorphic
to $Gr(E)^{\star\star}$, verifying a conjecture of Bando and Siu.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
18
The categories of this paper are: econ
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg