MINIMAL SURFACE SINGULARITIES ARE LIPSCHITZ NORMALLY EMBEDDED

International audienceAny germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. These two metrics are in general nonequivalent up to bilipschitz homeo-morphism. We show that minimal surface singularities are Lipschitz normally embedded, i.e., their outer and inner metrics are bilipschitz equivalent, and that they are the only rational surface singularities with this property. The proof is based on a preliminary result which gives a general characterization of Lipschitz normally embedded normal surface singularities