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A pinching theorem for cusps of negatively curved manifolds with finite volume


Author: Masahiko Kanai
Journal: Proc. Amer. Math. Soc. 107 (1989), 777-783
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1989-0937856-5
MathSciNet review: 937856
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Abstract: We give a new proof of the following theorem of M. Gromov: For a noncompact complete riemannian manifold $ M$ of negative curvature with finite volume, each cusp of $ M$ is diffeomorphic to $ N \times [0,\infty )$ with $ N$ being a compact flat space form provided that the sectional curvature of $ M$ satisfies the pinching condition $ - 4 < - {\Lambda ^2} \leq K \leq - 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0937856-5
Article copyright: © Copyright 1989 American Mathematical Society

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