Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CJM
Abstract view

# Hölder Compactification for Some Manifolds with Pinched Negative Curvature Near Infinity

Published:2008-12-01
Printed: Dec 2008
• Eric Bahuaud
• Tracey Marsh
 Format: HTML LaTeX MathJax PDF PostScript

## 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 $\MlK$. We use this to compactify $M$ and show that pinched negative sectional curvature outside $K$ implies $M$ has a compactification with a well-defined H\"older structure independent of $K$. The H\"older constant depends on the ratio of the curvature pinching. This extends and generalizes a 1985 result of Anderson and Schoen.
 MSC Classifications: 53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]

 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2015 : https://cms.math.ca/