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Hölder Compactification for Some Manifolds with Pinched Negative Curvature Near Infinity
Published online by Cambridge University Press: 20 November 2018
Abstract
We consider a complete noncompact Riemannian manifold $M$ and give conditions on a compact submanifold
$K\,\subset \,M$ so that the outward normal exponential map off the boundary of
$K$ is a diffeomorphism onto
$M\backslash K$. 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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- Research Article
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- Copyright © Canadian Mathematical Society 2008
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