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Remarks on the Yang-Mills flow on a compact Kähler manifold

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Collins T. C., Jacob A.

Universitatis Iagellonicae Acta Mathematica

2013

vol. 51

17-43

We study the Yang{Mills ow on a holomorphic vector bundle $E$ over a compact Kähler manifold $X$. We construct a natural barrier function along the ow, and introduce some techniques to study the blow-up of the curvature along the ow. Making some technical assumptions, we show how our techniques can be used to prove that the curvature of the evolved connection is uniformly bounded away from an analytic subvariety determined by the Harder-Narasimhan-Seshadri filtration of $E$. We also discuss how our assumptions are related to stability in some simple cases

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1 Universitatis Iagellonicae Acta Mathematica

1 2013

1 Collins T. C.

1 Jacob A.

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Remarks on the Yang-Mills flow on a compact Kähler manifold