On Hitchin's equations for cyclic G-Higgs bundles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916972469420032 |
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| author | Sagman, Nathaniel Tošić, Ognjen |
| author_facet | Sagman, Nathaniel Tošić, Ognjen |
| contents | 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 $\mathrm{E}_8.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hitchin's equations for cyclic G-Higgs bundles Sagman, Nathaniel Tošić, Ognjen Differential Geometry 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 $\mathrm{E}_8.$ |
| title | On Hitchin's equations for cyclic G-Higgs bundles |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.20853 |