# The Yang-Mills flow and the Atiyah-Bott formula on compact Kähler manifolds

@article{Jacob2011TheYF,
title={The Yang-Mills flow and the Atiyah-Bott formula on compact K{\"a}hler manifolds},
journal={American Journal of Mathematics},
year={2011},
volume={138},
pages={329 - 365}
}
• Published 7 September 2011
• Mathematics
• American Journal of Mathematics
We study the Yang-Mills flow on a holomorphic vector bundle $E$ over a compact K\"ahler manifold $X$. Along a solution of the flow, we show that the curvature endomorphism $i\Lambda F(A_t)$ 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… Expand
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