Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of the Yang-Mills Flow for Holomorphic Vector Bundles Over
  K\"ahler Manifolds: The Canonical Structure of the Limit   In the following article we study the limiting properties of the Yang-Mills
flow associated to a holomorphic vector bundle E over an arbitrary compact
K\"ahler manifold (X,{\omega}). In particular we show that the flow is
determined at infinity by the holomorphic structure of E. Namely, if we fix an
integrable unitary reference connection A_0 defining the holomorphic structure,
then the Yang-Mills flow with initial condition A_0, converges (away from an
appropriately defined singular set) in the sense of the Uhlenbeck compactness
theorem to a holomorphic vector bundle E_{\infty}, which is isomorphic to the
associated graded object of the Harder-Narasimhan-Seshadri filtration of
(E,A_0). Moreover, E_{\infty} extends as a reflexive sheaf over the singular
set as the double dual of the associated graded object. This is an extension of
previous work in the cases of 1 and 2 complex dimensions and proves the general
case of a conjecture of Bando and Siu.

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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol