Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms (Q2826651)

The authors consider a metric analogue of Zariski's multiplicity question: have two reduced hypersurface singularities, which are bi-Lipschitz \(\mathcal V\)-equivalent, the same multiplicity? They first show that the answer is yes if and only if the result holds for irreducible homogeneous polynomials. As corollary they obtain a positive answer for the case that all components of the tangent cone have isolated singularities, and for surface singularities without any restriction.