Journal of Differential Geometry

Minimal Volume Alexandrov Spaces

Peter A. Storm

Full-text: Open access

Abstract

Closed hyperbolic manifolds are proven to minimize volume over all Alexandrov spaces with curvature bounded below by −1 in the same bilipschitz class. As a corollary compact convex cores with totally geodesic boundary are proven to minimize volume over all hyperbolic manifolds in the same bilipschitz class. Also, closed hyperbolic manifolds minimize volume over all hyperbolic cone-manifolds in the same bilipschitz class with cone angles ≤ 2π. The proof uses techniques developed by Besson-Courtois-Gallot. In 3 dimensions, this result provides a partial solution to a conjecture in Kleinian groups concerning acylindrical manifolds.

Article information

Source
J. Differential Geom., Volume 61, Number 2 (2002), 195-225.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090351384

Digital Object Identifier
doi:10.4310/jdg/1090351384

Mathematical Reviews number (MathSciNet)
MR1972145

Zentralblatt MATH identifier
1070.53023

Citation

Storm, Peter A. Minimal Volume Alexandrov Spaces. J. Differential Geom. 61 (2002), no. 2, 195--225. doi:10.4310/jdg/1090351384. https://projecteuclid.org/euclid.jdg/1090351384


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