The limit of the Yang-Mills-Higgs flow on Higgs bundles

Abstract

In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a compact Kähler manifold $(M,\omega )$. We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorphic to the double dual of the graded Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle.

33 pages. arXiv admin note: text overlap with arXiv:math/0410055, arXiv:1206.5491 by other authors

References in corpus (1)

• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

Cited by in corpus (1)

• A note of semistable Higgs bundles over compact Kähler manifolds