Large-scale conformal rigidity in dimension three

Details Large-scale conformal rigidity in dimension three Large-scale conformal rigidity in dimension three

2002-10-28

arxiv.org/abs/math/0210433v1

Mathematics

Differential Geometry

22 pages, 2 figures

Scientific paper

We define a complete Riemannian manifold X to be large-scale conformally rigid if all groups that are quasi-isometric to some complete Riemannian manifold of bounded geometry conformal to X are quasi-isometric to X. We prove that many 3-manifolds, including Euclidean 3-space, hyperbolic 3-space and the product of the hyperbolic plane with the real line are large-scale conformally rigid. This implies new characterizations of groups that can act properly, cocompactly by isometries on those manifolds.

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