5,339 research outputs found
A finiteness theorem for hyperbolic 3-manifolds
We prove that there are only finitely many closed hyperbolic 3-manifolds with
injectivity radius and first eigenvalue of the Laplacian bounded below whose
fundamental groups can be generated by a given number of elements. An
application to arithmetic manifolds is also given.Comment: 20 pages, to appear in Journal of the London Mathematical Societ
Geometry and topology of complex hyperbolic and CR-manifolds
We study geometry, topology and deformation spaces of noncompact complex
hyperbolic manifolds (geometrically finite, with variable negative curvature),
whose properties make them surprisingly different from real hyperbolic
manifolds with constant negative curvature. This study uses an interaction
between K\"ahler geometry of the complex hyperbolic space and the contact
structure at its infinity (the one-point compactification of the Heisenberg
group), in particular an established structural theorem for discrete group
actions on nilpotent Lie groups
Hyperplane arrangements in negatively curved manifolds and relative hyperbolicity
We show that certain aspherical manifolds arising from hyperplane
arrangements in negatively curved manifolds have relatively hyperbolic
fundamental group.Comment: 27 pages, minor changes, to appear in Groups, Geometry, and Dynamic
Deformations and stability in complex hyperbolic geometry
This paper concerns with deformations of noncompact complex hyperbolic
manifolds (with locally Bergman metric), varieties of discrete representations
of their fundamental groups into and the problem of (quasiconformal)
stability of deformations of such groups and manifolds in the sense of L.Bers
and D.Sullivan.
Despite Goldman-Millson-Yue rigidity results for such complex manifolds of
infinite volume, we present different classes of such manifolds that allow
non-trivial (quasi-Fuchsian) deformations and point out that such flexible
manifolds have a common feature being Stein spaces. While deformations of
complex surfaces from our first class are induced by quasiconformal
homeomorphisms, non-rigid complex surfaces (homotopy equivalent to their
complex analytic submanifolds) from another class are quasiconformally
unstable, but nevertheless their deformations are induced by homeomorphisms
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