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arXiv · 2410.20853

On Hitchin's equations for cyclic G-Higgs bundles

Nathaniel Sagman·Ognjen Tošić
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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 $\mathrm{E}_8.$

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Nathaniel Sagman, Ognjen Tošić. 2024-10-28. On Hitchin's equations for cyclic G-Higgs bundles. https://arxiv.org/abs/2410.20853

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