Orbifold finiteness under geometric and spectral constraints

Abstract

The class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is finite up to orbifold homeomorphism.

11 pages. V2 only adds the following comment: that the material in this article has now been inserted, without substantial changes, in arXiv:1401.0531, which has now been published in the Journal of Geometric Analysis

References in corpus (2)

• Orbifold homeomorphism finiteness based on geometric constraints
• G-actions with close orbit spaces

Cited by in corpus (4)

• Introduction to orbifolds
• Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces
• G-actions with close orbit spaces
• A Toponogov globalisation result for Lorentzian length spaces