Riemann surfaces上扭曲Higgs对的Yang-Mills-Higgs流的收敛性
Convergence of Yang-Mills-Higgs flow for twist Higgs pairs on Riemann surfaces
摘要：
本文研究了黎曼曲面$X$上厄米向量丛$(E,H_0)$上扭曲Higgs对的Yang-Mills-Higgs泛函的梯度流.已知具有初始数据$(A_0,ϕ_0)$的梯度流收敛于该泛函的临界点$(A_\infty, ϕ_\infty)$。利用一个修正的Chern-Weil型不等式，证明了极限扭曲Higgs丛$(E, d_{A_\infty}", ϕ_\infty)$是由初始扭曲Higgs丛$(E,d_{A_0}",ϕ_0)$的Harder-Narasimhan-Seshadri过滤定义的分次扭曲Higgs丛给出的，推广了Wilkin关于非扭曲Higgs丛的结果.
英文摘要：
We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Riemann surface $X$. It is already known the gradient flow with initial data $(A_0,ϕ_0)$ converges to a critical point $(A_\infty, ϕ_\infty)$ of this functional. Using a modified Chern-Weil type inequality, we prove that the limiting twist Higgs bundle $(E, d_{A_\infty}", ϕ_\infty)$ is given by 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.
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