The geometry of maximal representations of surface groups into \(\mathrm{SO}_0(2,n)\)

DOI10.1215/00127094-2019-0052OpenAlexW3105350178MaRDI QIDQ2280562

Nicolas Tholozan, Brian Collier, Jérémy Toulisse

Publication date: 18 December 2019

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.08799

zbMATH Keywords

geometric structuresHiggs bundlespseudo-Riemannian geometryAnosov representationsmaximal representations

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) General geometric structures on low-dimensional manifolds (57M50) Vector bundles on curves and their moduli (14H60) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (22)

Non-uniqueness of minimal surfaces in a product of closed Riemann surfaces ⋮ Exotic components of \(\mathrm{SO}(p, q)\) surface group representations, and their Higgs bundle avatars ⋮ Studying deformations of Fuchsian representations with Higgs bundles ⋮ On the irreducible action of \(\mathrm{PSL}(2, \mathbb{R})\) on the 3-dimensional Einstein universe ⋮ Global properties of some weight 3 variations of Hodge structure ⋮ Anosov representations with Lipschitz limit set ⋮ Hausdorff dimension of limit sets for projective Anosov representations ⋮ Working session: Higher rank Teichmüller theory. Abstracts from the working session held October 9--14, 2022 ⋮ Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces ⋮ Boundary of the Gothen components ⋮ Domination results in n$n$‐Fuchsian fibers in the moduli space of Higgs bundles ⋮ Cyclic Higgs bundles and minimal surfaces in pseudo-hyperbolic spaces ⋮ Length spectrum compactification of the \(\mathrm{SO}_0(2, 3)\)-Hitchin component ⋮ Twisted cyclic quiver varieties on curves ⋮ Riemannian metrics on the moduli space of GHMC anti-de Sitter structures ⋮ Moduli spaces of Higgs bundles - old and new ⋮ Anti-de Sitter Geometry and Teichmüller Theory ⋮ On cyclic Higgs bundles ⋮ The moduli spaces of equivariant minimal surfaces in \({\mathbb {RH}}^3\) and \(\mathbb {RH}^4\) via Higgs bundles ⋮ Higgs bundles and higher Teichmüller spaces ⋮ Flat surfaces and algebraic curves. Abstracts from the workshop held September 16--22, 2018 ⋮ The half-space model of pseudo-hyperbolic space

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