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 K\ahler 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.