Hölder Compactification for some manifolds with pinched negative curvature near infinity

Eric Bahuaud; Tracey Marsh

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Hölder Compactification for some manifolds with pinched negative curvature near infinity

Eric Bahuaud·Tracey Marsh

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Abstract

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.

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BibTeX RIS

Eric Bahuaud, Tracey Marsh. 2006-01-20. Hölder Compactification for some manifolds with pinched negative curvature near infinity. https://arxiv.org/abs/math/0601503

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