, Volume 53, Issue 2, pp 379-397,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 15 Dec 2011

Quotient metrics with applications in convex geometry

Abstract

Burago et al. (Graduate studies in mathematics, AMS, 2001) considered quotient metric spaces consisting of orbits with respect to some isometry groups. We extend their approach over some semigroups of transformations. We are concerned with quotient semi-metrics in spaces of generalized orbits and give conditions sufficient for these semi-metrics to be metrics. We apply our approach to hyperspaces of compact convex subsets of Euclidean n-space and to that of convex bodies, endowed, respectively, with the Hausdorff metric and with the symmetric difference metric.

An erratum to this article can be found at http://dx.doi.org/10.1007/s13366-012-0115-5.