An introduction to Higgs bundles via harmonic maps

DOI10.3842/SIGMA.2019.035zbMath1419.53064arXiv1809.05747WikidataQ127915088 ScholiaQ127915088MaRDI QIDQ2003549

Qiongling Li

Publication date: 9 July 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.05747

zbMATH Keywords

harmonic mapsHiggs bundlesnon-abelian Hodge correspondence

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Differential geometric aspects of harmonic maps (53C43) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Related Items (11)

Non-abelian Hodge theory and related topics ⋮ Asymptotics for minimizers of a Donaldson functional and mean curvature 1-immersions of surfaces into hyperbolic 3-manifolds ⋮ Harmonic metrics of generically regular semisimple Higgs bundles on noncompact Riemann surfaces ⋮ Working session: Higher rank Teichmüller theory. Abstracts from the working session held October 9--14, 2022 ⋮ The covariance metric in the Blaschke locus ⋮ Domination results in n$n$‐Fuchsian fibers in the moduli space of Higgs bundles ⋮ Meromorphic parahoric Higgs torsors and filtered Stokes G-local systems on curves ⋮ Length spectrum compactification of the \(\mathrm{SO}_0(2, 3)\)-Hitchin component ⋮ Moduli spaces of Higgs bundles - old and new ⋮ Equivariant harmonic maps depend real analytically on the representation ⋮ Strict plurisubharmonicity of the energy on Teichmüller space associated to Hitchin representations

Cites Work

• And Then There Were None

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