## Illinois Journal of Mathematics

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

### A comparison theorem on simply connected complete Riemannian manifolds

#### 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