A Restriction for Singularities on Collapsing Orbifolds

Abstract EN

Every point p in an orbifold X has a neighborhood that is homeomorphic to Gp∖Br(0), where Gp is a finite group acting on Br(0)⊂ℝn, so that Gp(0)=0.

Assume X is a Riemannian orbifold with isolated singularities that is collapsing, that is, X admits a sequence of metrics gi with uniformly bounded curvature, so that, for any x∈X, the volume of B1(x), with respect to the metric gi, goes to 0 as i→∞.

For such X, we prove that |Gp|≤(2π/0.47)n(n−1) for all singularities p∈X.