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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 (A 0, ϕ 0) 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, \(d''_{A_0 }\), ϕ 0), generalizing Wilkin’s results for untwist Higgs bundle.

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