Orbifolds and Manifold Quotients with Upper Curvature Bounds

Abstract

We characterize Riemannian orbifolds with an upper curvature bound in the Alexandrov sense as reflectofolds, i.e., Riemannian orbifolds all of whose local groups are generated by reflections, with the same upper bound on the sectional curvature. Combined with a result by Lytchak–Thorbergsson this implies that a quotient of a Riemannian manifold by a closed group of isometries has locally bounded curvature (from above) in the Alexandrov sense if and only if it is a reflectofold.