Rigidity of minimal volume Alexandrov spaces

Details Rigidity of minimal volume Alexandrov spaces Rigidity of minimal volume Alexandrov spaces

2005-04-22

arxiv.org/abs/math/0504473v2

Ann. Acad. Sci. Fenn. Math. 31 (2006) 381--389

Mathematics

Geometric Topology

Scientific paper

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.

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