Bilipschitz geometry of real surface singularities whose tangent cone is a plane

Abstract: Tangent cones are preserved under ambient bilipschitz equivalence, but the behavior of the Nash cone is more delicate. This paper explores the behavior of the Nash cone and of exceptional rays under ambient bilipschitz equivalence for real surfaces in $\mathbb R<sup>3$ with isolated singularity and whose tangent cone is a plane.