Minimal volume Alexandrov spaces

Details Minimal volume Alexandrov spaces Minimal volume Alexandrov spaces

2001-12-11

arxiv.org/abs/math/0112095v3

J. Differential Geom. 61 (2002) 195-226

Mathematics

Geometric Topology

22 pages

Scientific paper

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 not greater than 2pi. 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.

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