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ISRN Geometry
Volume 2011 (2011), Article ID 502814, 7 pages
doi:10.5402/2011/502814
A Restriction for Singularities on Collapsing Orbifolds
Department of Mathematics and Statistics, California State University, Long Beach, CA 90840, USA
Received 8 August 2011; Accepted 5 September 2011
Academic Editors: S. Kar, U. Lindström, and E. H. Saidi
Copyright © 2011 Yu Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Every point in an orbifold has a neighborhood that is homeomorphic to , where is a finite group acting on , so that . Assume is a Riemannian orbifold with isolated singularities that is collapsing, that is, admits a sequence of metrics with uniformly bounded curvature, so that, for any , the volume of , with respect to the metric , goes to 0 as . For such , we prove that for all singularities .