Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms

TL;DR

This paper investigates how the multiplicity of complex analytic surface singularities in three-dimensional space behaves under bi-Lipschitz homeomorphisms, providing partial answers to a metric version of Zariski's multiplicity conjecture.

Contribution

It proves that the multiplicity of complex analytic surface singularities in ^3 is invariant under bi-Lipschitz homeomorphisms, advancing understanding of metric invariants in singularity theory.

Findings

Multiplicity in ^3 is a bi-Lipschitz invariant.

Partial progress on a metric version of Zariski's conjecture.

Focus on non-isolated surface singularities.

Abstract

We give partial answers to a metric version of Zariski's multiplicity conjecture. In particular, we prove the multiplicity of complex analytic surface (not necessarily isolated) singularities in $\mathbb{C}^3$ is a bi-Lipschitz invariant.