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

作　　者：ZHANG Wei 

机构地区：[1]Department of Mathematics, South China University of Technology

出　　处：《Science China Mathematics》2014年第8期1657-1670,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11101393 and 11201447)

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.

关 键 词：twist Higgs bundle Yang-Mills-Higgs flow Harder-Narasimhan-Seshadri filtration Chern-Weil formula 

分 类 号：O186.12[理学—数学]