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...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11101393 and 11201447)
文摘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.
