We study invariance of multiplicity of complex analytic germs and degree of complex affine
sets under outer bi‐Lipschitz transformations (outer bi‐Lipschitz homeomorphims of germs …

The multiplicity of an algebraic curve C in the complex plane at a point p on that curve is
defined as the number of points that occur at the intersection of C with a general complex …

We show that for every $ k\ge 3$ there exist complex algebraic cones of dimension $ k $
with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they …

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 …

In this article, we prove that for a definable set in an o-minimal structure with connected link
(at 0 or infinity), the inner distance of the link is equivalent to the inner distance of the set …

Let $ X\subset\mathbb {C}^ n; Y\subset\mathbb {C}^ m $ be closed affine varieties and let
$\phi: X\to Y $ be an algebraic bi-Lipschitz homeomorphism. Then ${\rm deg}\X={\rm deg}\Y …

We address a metric version of Zariski's multiplicity conjecture at infinity that says that two
complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the …

In this paper, we prove the Fukui–Kurdyka–Paunescu conjecture, which says that sub-
analytic arc-analytic bi-Lipschitz homeomorphisms preserve the multiplicities of real analytic …

We prove that if two germs of plane curves (C, 0) and (C′, 0) with at least one singular
branch are equivalent by a (real) smooth diffeomorphism, then C is complex isomorphic to …

In this article, we prove that for a definable set in an o‐minimal structure with connected link
(at 0 or infinity), the inner distance of the link is equivalent to the inner distance of the set …