# Analytic convergence of harmonic metrics for parabolic Higgs bundles

## TL;DR

This paper proves that harmonic metrics for parabolic Higgs bundles depend analytically on weights and bundle stability, extending classical results on hyperbolic cone metrics and their parametrization.

## Contribution

It establishes the analytic dependence of harmonic metrics on weights and stability for parabolic Higgs bundles, generalizing McOwen and Judge's theorems.

## Key findings

- Harmonic metrics depend analytically on weights and stability.
- Extension of McOwen's theorem to Higgs bundles.
- Generalization of Judge's analytic parametrization result.

## Abstract

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.