Convergence of Yang-Mills-Higgs flow for twist Higgs pairs on Riemann surfaces

Abstract

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle (E,H) over Riemann surface X. It is already known the gradient flow with initial data (A0, ϕ0) converges to a critical point (A∞, ϕ∞). Using a modified Chern-Weil type inequality, we prove that the limiting twist Higgs bundle (E, \(d''_{A_\infty }\)ϕ∞) coincides with the graded twist Higgs bundle defined by the Harder-Narasimhan-Seshadri filtration of the initial twist Higgs bundle (E, \(d''_{A_0 }\), ϕ0), generalizing Wilkin’s results for untwist Higgs bundle.