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

Abstract

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 $(A_0,{\varphi }_0)$ converges to a critical point $(A_{\infty },{\varphi }_{\infty })$ of this functional. Using a modified Chern-Weil type inequality, we prove that the limiting twist Higgs bundle $(E,d_{A_{\infty }}",{\varphi }_{\infty })$ is given by the graded twist Higgs bundle defined by the Harder-Narasimhan-Seshadri filtration of the initial twist Higgs bundle $(E,d_{A_0}",{\varphi }_0)$, generalizing Wilkin's results for untwist Higgs bundle.

19 pages, 1 figure. arXiv admin note: text overlap with arXiv:math/0410055, arXiv:math/0611113 by other authors

References in corpus (1)

• Mirror symmetry, Langlands duality, and the Hitchin system