Milnor's fibration theorem is about the geometry and topology of real and complex analytic
maps near their critical points, a ubiquitous theme in mathematics. As such, after 50 years …

We describe the Lipschitz geometry of complex curves. For the most part this is well known
material, but we give a stronger version even of known results. In particular, we give a quick …

A semi-algebraic subset in R^ n R n or C^ n C n is naturally equipped with two different
metrics, the inner metric and the outer metric. Such a set (or its germ) is called Lipschitz …

We prove that the outer Lipschitz geometry of a germ $(X, 0) $ of a normal complex surface
singularity determines a large amount of its analytic structure. In particular, it follows that any …

Abstract Any subanalytic germ (X, 0)⊂(ℝ n, 0) is equipped with two natural metrics: its outer
metric, induced by the standard Euclidean metric of the ambient space, and its inner metric …

We prove that tangent cones of Lipschitz normally embedded sets are Lipschitz normally
embedded. We also extend to real subanalytic sets the notion of reduced tangent cone and …

This paper is devoted to study multiplicity and regularity as well as to present some
classifications of complex analytic sets. We present an equivalence for complex analytical …

These notes deal with semialgebraic and subanalytic subsets of ℝ n, and more generally
with all the sets that are definable in a polynomially bounded o-minimal structure expanding …

Let X_o be a complex weighted-homogeneous complete intersection germ,(possibly non-
reduced). Let X be a perturbation of X_o by``higher-order-terms". We give sufficient criteria …

Two subset germs of Euclidean spaces are called blow-spherically equivalent if their
spherical modifications are homeomorphic and the homeomorphism induces …