Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces : Review (Topology and Analysis of Discrete Groups and Hyperbolic Spaces)

Abstract

Let (E, overline{partial}_{E}, $theta$) be a stable Higgs bundle of degree 0 on a compact Riemann surface X. We have the associated family of harmonic bundles (E, overline{partial}_{E}, t $theta$, h_{t}) (t in mathbb{C}^{*}). We briefly review the study of the asymptotic behaviour of this family when t goes to infty.