Hölder Compactification for some manifolds with pinched negative curvature near infinity

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We consider a complete noncompact Riemannian manifold M and give conditions on a compact submanifold K of M so that the outward normal exponential map off of the boundary of K is a diffeomorphism onto M\K. We use this to compactify M and show that pinched negative sectional curvature outside K implies M has a compactification with a well defined Hölder structure independent of K. The Hölder constant depends on the ratio of the curvature pinching. This extends and generalizes a 1985 result of Anderson and Schoen.
27 pages, 1 figure

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Differential Geometry, 53C20

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http://salesiana.dossiersoluciones.com/handle/123456789/107637

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601503
 http://arxiv.org/abs/math/0601503

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arXiv