Quasi-Fuchsian manifolds with particles

Details Quasi-Fuchsian manifolds with particles Quasi-Fuchsian manifolds with particles

2006-03-17

arxiv.org/abs/math/0603441v3

Mathematics

Differential Geometry

Now 48 pages, no figure. v2: new title, various corrections, results extended to include graph singularities ("interacting par

Scientific paper

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than $\pi$: any first-order deformation changes either one of those angles or the conformal structure at infinity, with marked points corresponding to the endpoints of the singular lines. Moreover, any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone-manifold structure.

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