Illinois Journal of Mathematics

A comparison theorem on simply connected complete Riemannian manifolds

Ana Granados

Full-text: Open access

Abstract

We consider simply connected complete Riemannian manifolds with sectional curvature bounded above by $-C^2 < 0$, and curves on such manifolds with geodesic curvature at most $C>0$ in absolute value. We give an estimate for the rate at which such curves approach the boundary of the manifold.

Article information

Source
Illinois J. Math., Volume 47, Number 4 (2003), 1167-1176.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138097

Digital Object Identifier
doi:10.1215/ijm/1258138097

Mathematical Reviews number (MathSciNet)
MR2036996

Zentralblatt MATH identifier
1045.53027

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)

Citation

Granados, Ana. A comparison theorem on simply connected complete Riemannian manifolds. Illinois J. Math. 47 (2003), no. 4, 1167--1176. doi:10.1215/ijm/1258138097. https://projecteuclid.org/euclid.ijm/1258138097


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