Bi-Lipschitz geometry of weighted homogeneous surface singularities

Abstract

We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent but not bi-Lipschitz equivalent.

5 pages. Added result that nonhomogeneous cyclic quotients are not conical