Analytic convergence of harmonic metrics for parabolic Higgs bundles

作者：Kim Semin; Wilkin Graeme^*

来源：Journal of Geometry and Physics, 2018, 127: 55-67.

DOI：10.1016/j.geomphys.2018.01.023

• Parabolic Higgs bundles
• Hyperbolic surfaces
• Harmonic metrics

In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric depends analytically on the weights and the stable Higgs bundle. This gives a Higgs bundle generalisation of a theorem of McOwen on the existence of hyperbolic cone metrics on a punctured surface within a given conformal class, and a generalisation of a theorem of Judge on the analytic parametrisation of these metrics.

• 出版日期2018-4