Geodesic
The gradient flow of Higgs pairs
Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1373-1422.

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In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional of Higgs pairs on a Hermitian vector bundle (E,H0​) over a Kähler surface (M,ω), and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition (A0​,φ0​) converges, in an appropriate sense which takes into account bubbling phenomena, to a critical points (A∞​,φ∞​) of this functional. We also prove that the limiting Higgs pair (A∞​,φ∞​) can be extended smoothly to a vector bundle E∞​ over (M,ω) , and the isomorphism class of the limiting Higgs bundle (E∞​,A∞​,φ∞​) is given by the double dual of the graded Higgs sheaves associate to Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle (E,A0​,φ0​).
DOI : 10.4171/jems/284
Classification : 53-XX, 58-XX, 00-XX
Keywords: Higgs bundles, Kähler surface, Harder–Narasimhan–Seshadri filtration 
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     author = {Jiayu Li and Xi Zhang},
     title = {The gradient flow of {Higgs} pairs},
     journal = {Journal of the European Mathematical Society},
     pages = {1373--1422},
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     volume = {13},
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     year = {2011},
     doi = {10.4171/jems/284},
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Jiayu Li; Xi Zhang. The gradient flow of Higgs pairs. Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1373-1422. doi : 10.4171/jems/284. http://geodesic.mathdoc.fr/articles/10.4171/jems/284/

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