Geodesic
Hölder Compactification for Some Manifolds with Pinched Negative Curvature Near Infinity
Canadian journal of mathematics, Tome 60 (2008) no. 6, pp. 1201-1218

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2008-051-6
Mots-clés : 53C20 
Bahuaud, Eric. Hölder Compactification for Some Manifolds with Pinched Negative Curvature Near Infinity. Canadian journal of mathematics, Tome 60 (2008) no. 6, pp. 1201-1218. doi: 10.4153/CJM-2008-051-6
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[AS85] Anderson, M. T. and Schoen, R., Positive harmonic functions on complete manifolds of negative curvature. Ann. of Math. 121(1985), no. 3, 4219–461. Google Scholar

[EO73] Eberlein, P. and O’Neill, B., Visibility manifolds. Pacific J. Math. 46(1973), 45–109. Google Scholar

[Kli95] Klingenberg, W. P. A., Riemannian Geometry. Second edition. de Gruyter Studies in Mathematics 1,Walter de Gruyter, Berlin, 1995. Google Scholar

[Pet98] Petersen, P., Riemannian Geometry. Graduate Texts inMathematics 171, Springer-Verlag, New York, 1998. Google Scholar

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