The gradient flow of Higgs pairs

Li, Jiayu, and Zhang, Xi. "The gradient flow of Higgs pairs." Journal of the European Mathematical Society 013.5 (2011): 1373-1422. <http://eudml.org/doc/277241>.

@article{Li2011,
abstract = {We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Kähler surface $(M,\omega )$, and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition $(A_0,\phi _0)$ converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point $(A_\infty ,\phi _\infty )$ of this functional. We also prove that the limiting Higgs pair $(A_\infty ,\phi _\infty )$ can be extended smoothly to a vector bundle $E_\infty $ over $(M,\omega )$, and the isomorphism class of the limiting Higgs bundle $(E_\infty ,A_\infty \phi _\infty )$ is given by the double dual of the graded Higgs sheaves associated to the Harder–Narasimhan–Seshadri filtration of the initial Higgs bundle $(E,A_0,\phi _0)$.},
author = {Li, Jiayu, Zhang, Xi},
journal = {Journal of the European Mathematical Society},
keywords = {Higgs bundles; Kähler surface; Harder–Narasimhan–Seshadri filtration; Higgs bundles, Kähler surface, Harder-Narasimhan-Seshadri filtration},
language = {eng},
number = {5},
pages = {1373-1422},
publisher = {European Mathematical Society Publishing House},
title = {The gradient flow of Higgs pairs},
url = {http://eudml.org/doc/277241},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Li, Jiayu
AU - Zhang, Xi
TI - The gradient flow of Higgs pairs
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 5
SP - 1373
EP - 1422
AB - We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Kähler surface $(M,\omega )$, and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition $(A_0,\phi _0)$ converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point $(A_\infty ,\phi _\infty )$ of this functional. We also prove that the limiting Higgs pair $(A_\infty ,\phi _\infty )$ can be extended smoothly to a vector bundle $E_\infty $ over $(M,\omega )$, and the isomorphism class of the limiting Higgs bundle $(E_\infty ,A_\infty \phi _\infty )$ is given by the double dual of the graded Higgs sheaves associated to the Harder–Narasimhan–Seshadri filtration of the initial Higgs bundle $(E,A_0,\phi _0)$.
LA - eng
KW - Higgs bundles; Kähler surface; Harder–Narasimhan–Seshadri filtration; Higgs bundles, Kähler surface, Harder-Narasimhan-Seshadri filtration
UR - http://eudml.org/doc/277241
ER -