Deformations of hyperbolic structures

DOI10.1017/S030500410006343XzbMath0577.53041OpenAlexW2101501034MaRDI QIDQ3697855

Christos Kourouniotis

Publication date: 1985

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s030500410006343x

zbMATH Keywords

totally geodesichyperbolic spaceKleinian groupsquasi-Fuchsian groupsquasiconformal deformationsbending deformations

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Global submanifolds (53C40) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (19)

Deformations of representations of discrete subgroups of \(SO(3,1)\) ⋮ Branched \(\mathbb{C} P^ 1\)-structures on surfaces with prescribed real holonomy ⋮ From Hyperbolic Dehn Filling to Surgeries in Representation Varieties ⋮ The geometry of Nielsen's hull for a Kleinian group in space and quasi- conformal mappings ⋮ A rigidity theorem for Möbius groups ⋮ Quasi-fuchsian structures on hyperbolic 3-manifolds admitting a decomposition into ideal tetrahedra ⋮ Singular pleated surfaces and CP¹–structures ⋮ Bending and stamping deformations of hyperbolic manifolds ⋮ Topological aspects of conformally flat manifolds ⋮ Constant scalar curvature hypersurfaces in \((3 + 1)\)-dimensional GHMC Minkowski spacetimes ⋮ Quakebend deformations in complex hyperbolic quasi-Fuchsian space ⋮ Bending in the space of quasi-Fuchsian structures ⋮ Local rigidity of discrete groups acting on complex hyperbolic space ⋮ Recovering the geometry of a flat spacetime from background radiation ⋮ Quasi-Fuchsian Co-Minkowski Manifolds ⋮ Boundary conformal field theories, limit sets of Kleinian groups and holography ⋮ Local rigidity of hyperbolic 3-manifolds after Dehn surgery ⋮ Nonstandard uniformized conformal structures on hyperbolic manifolds ⋮ Group actions, Teichmüller spaces and cobordisms

Cites Work

• The Fenchel-Nielsen deformation
• On the first Betti number of a constant negatively curved manifold
• The geometry of finitely generated Kleinian groups
• Remarks on the cohomology of groups
• Rings and Quasiconformal Mappings in Space
• Discrete Subgroups of the Lorentz Group.

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