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arXiv · 1403.8037

Limiting behavior of Donaldson's heat flow on non-Kähler surfaces

Jacob McNamara·Yifei Zhao
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Abstract

Let $X$ be a compact Hermitian surface, and $g$ be any fixed Gauduchon metric on $X$. Let $E$ be an Hermitian holomorphic vector bundle over $X$. On the bundle $E$, Donaldson's heat flow is gauge equivalent to a flow of holomorphic structures. We prove that this flow converges, in the sense of Uhlenbeck, to the double dual of the graded sheaf associated to the $g$-Harder-Narasimhan-Seshadri filtration of $X$. This result generalizes a convergence theorem of Daskalopoulos and Wentworth to non-Kähler setting.

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Jacob McNamara, Yifei Zhao. 2014-03-31. Limiting behavior of Donaldson's heat flow on non-Kähler surfaces. https://arxiv.org/abs/1403.8037

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