Rigidity of minimal volume Alexandrov spaces
Geometric Topology
2009-03-10 v2
Abstract
Let Z be an Alexandrov space with curvature bounded below by -1 such that Z is homotopy equivalent to a real hyperbolic manifold M. It is known that the volume of Z is not smaller than the volume of M. If the volumes are equal, this short paper proves that the homotopy equivalence is homotopic to an isometric homeomorphism. The main analytic tool is a theorem of Reshetnyak about quasiregular maps.
Keywords
Cite
@article{arxiv.math/0504473,
title = {Rigidity of minimal volume Alexandrov spaces},
author = {Peter A. Storm},
journal= {arXiv preprint arXiv:math/0504473},
year = {2009}
}