A restriction for singularities on collapsing orbifolds

Abstract

An orbifold $X$ is locally homeomorphic to $G_x\backslash B_r(0)$, where $G_x$ is a finite group acting on $B_r(0)\subset {\mathbb{R}}^n$, so that $G_x(0)=0$. For collapsing orbifolds with isolated singularities, we show there is a uniform bound in $|G_x|$.

Preprint. 9 pages. The bound for $|G_x|$ is corrected to $(2\pi /0.47{)}^{n(n-1)}$