Harmonic maps and representations of non-uniform lattices of \(PU(m,1)\)

DOI10.5802/aif.2359zbMath1147.22009arXivmath/0309193OpenAlexW1528549776MaRDI QIDQ931892

Vincent Koziarz, Julien Maubon

Publication date: 4 July 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309193

zbMATH Keywords

rigidityrepresentationsharmonic mapscomplex hyperbolic spacenon-uniform latticessurfaces of finite topological typeToledo invariants

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Differential geometric aspects of harmonic maps (53C43) Rigidity results (53C24) Kähler-Einstein manifolds (32Q20) Differential geometry of symmetric spaces (53C35) Negative curvature complex manifolds (32Q05)

Related Items

NATURAL MAPS FOR MEASURABLE COCYCLES OF COMPACT HYPERBOLIC MANIFOLDS ⋮ Bounded differential forms, generalized Milnor-Wood inequality and an application to deformation rigidity ⋮ Almost strict domination and anti‐de Sitter 3‐manifolds ⋮ Infinite energy harmonic maps from Riemann surfaces to CAT(0) spaces ⋮ Infinite energy equivariant harmonic maps, domination, and anti-de Sitter \(3\)-manifolds ⋮ Volume invariant and maximal representations of discrete subgroups of Lie groups ⋮ Integrality of volumes of representations ⋮ Maximal representations of complex hyperbolic lattices into \(\mathrm{SU}(m,n)\) ⋮ Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type ⋮ Surface group representations with maximal Toledo invariant ⋮ Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups ⋮ Rigidity at infinity for lattices in rank-one Lie groups ⋮ Superrigidity of maximal measurable cocycles of complex hyperbolic lattices ⋮ Local quaternionic rigidity for complex hyperbolic lattices ⋮ Kähler groups, real hyperbolic spaces and the Cremona group. With an appendix by Serge Cantat

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local rigidity of discrete groups acting on complex hyperbolic space
• Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups
• Harmonic mappings of Kähler manifolds to locally symmetric spaces
• The complex-analyticity of harmonic maps and the strong rigidity of compact Kaehler manifolds
• Representations of surface groups in complex hyperbolic space
• Flat G-bundles with canonical metrics
• Archimedean superrigidity and hyperbolic geometry
• On univalent harmonic maps between surfaces
• Geometric superrigidity
• Harmonic maps, hyperbolic cohomology and higher Milnor inequalities
• Complete surfaces of at most quadratic area growth
• Harmonic maps of infinite energy and rigidity results for representations of fundamental groups of quasiprojective varieties
• Complex hyperbolic quasi-Fuchsian groups and Toledo's invariant
• Continuous bounded cohomology and applications to rigidity theory
• Harmonic maps into singular spaces and \(p\)-adic superrigidity for lattices in groups of rank one
• Representations of free Fuchsian groups in complex hyperbolic space
• L//2 cohomology of warped products and arithmetic groups
• Cusp closing in rank one symmetric spaces
• Kähler manifolds and 1/4-pinching
• A special Stoke's theorem for complete Riemannian manifolds
• Harmonic maps from surfaces to certain Kaehler manifolds.
• Some properties and applications of harmonic mappings
• Holomorphicity of Certain Harmonic Maps from a Surface to Complex Projective n -Space
• Métriques d'Einstein à cusps et équations de Seiberg-Witten.
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
• Harmonic Mappings of Riemannian Manifolds