On Hitchin's equations for cyclic G-Higgs bundles

Nathaniel Sagman; Ognjen Tošić

On Hitchin's equations for cyclic G-Higgs bundles

Differential Geometry 2025-09-30 v2

Authors: Nathaniel Sagman , Ognjen Tošić

Abstract

We develop a Lie-theoretic perspective on Hitchin's equations for cyclic $G$ -Higgs bundles, which we use to study analytic and geometric properties of harmonic maps. Among other things, we prove Dai-Li's conjecture on the monotonicity of the energy density in the case of Coxeter cyclic $G$ -Higgs bundles, for all $G$ , and Dai-Li's negative curvature conjecture for Coxeter cyclic $G$ -Higgs bundles, for all $G$ except those of type $\mathrm{E}_7$ and $\mathrm{E}_8.$

Keywords

Hitchin's equations cyclic G-Higgs bundles harmonic maps Dai-Li's conjecture energy density negative curvature conjecture

Cite

@article{arxiv.2410.20853,
  title  = {On Hitchin's equations for cyclic G-Higgs bundles},
  author = {Nathaniel Sagman and Ognjen Tošić},
  journal= {arXiv preprint arXiv:2410.20853},
  year   = {2025}
}

On Hitchin's equations for cyclic G-Higgs bundles

Abstract

Keywords

Cite

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