A restriction for singularities on collapsing orbifolds
type: Item
instance of: scholarly article
title: A restriction for singularities on collapsing orbifolds
zbMATH Open document ID: 1239.58023
DOI: 10.5402/2011/502814
published in: ISRN Geometry
publication date: 2012-05-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1101.4444
review text: Summary: Every point \(p\) in an orbifold \(X\) has a neighborhood that is homeomorphic to \(G_p \setminus B_r(0)\), where \(G_p\) is a finite group acting on \(B_r(0) \subset \mathbb R^n\), so that \(G_p(0) = 0\). Assume \(X\) is a Riemannian orbifold with isolated singularities that is collapsing, that is, \(X\) admits a sequence of metrics \(g_i\) with uniformly bounded curvature, so that, for any \(x \in X\), the volume of \(B_1(x)\), with respect to the metric \(g_i\), goes to \(0\) as \(i \rightarrow \infty\). For such \(X\), we prove that \(|G_p| \leq (2\pi/0.47)^{n(n-1)}\) for all singularities \(p \in X\).
Mathematics Subject Classification ID: 58K30
zbMATH DE Number: 6031932
MaRDI profile type: Publication
OpenAlex ID: W2109670649
Wikidata QID: Q58689542
arXiv ID: 1101.4444
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author: Yu Ding
description: scientific article; zbMATH DE number 6031932