摘要
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∞,φ∞)coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle(E,d′′A0,φ0),generalizing Wilkin’s results for untwist Higgs bundle.
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∞, φ∞） coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle（E, d＂A0, φ0）, generalizing Wilkin＇s results for untwist Higgs bundle.
基金
supported by National Natural Science Foundation of China(Grant Nos.11101393 and 11201447)
