A restriction for singularities on collapsing orbifolds
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 \(p \in X\).
scientific article; zbMATH DE number 6031932
scientific article