Journal of Differential Geometry

Cones Embedded in Hyperbolic Manifolds

Andrew Przeworski

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Abstract

We show that the existence of a maximal embedded tube in a hyperbolic n-manifold implies the existence of a certain conical region. One application is to establish a lower bound on the volume of the region outside the tube, thereby improving estimates on volume and estimates on lengths of geodesics in small volume hyperbolic 3-manifolds. We also provide new bounds on the injectivity radius and diameter of an n-manifold.

Article information

Source
J. Differential Geom., Volume 58, Number 2 (2001), 219-232.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090348325

Digital Object Identifier
doi:10.4310/jdg/1090348325

Mathematical Reviews number (MathSciNet)
MR1913942

Zentralblatt MATH identifier
1050.57013

Citation

Przeworski, Andrew. Cones Embedded in Hyperbolic Manifolds. J. Differential Geom. 58 (2001), no. 2, 219--232. doi:10.4310/jdg/1090348325. https://projecteuclid.org/euclid.jdg/1090348325


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