%0 Journal Article
%T Lipschitz geometry of complex curves
%+ Columbia University [New York]
%+ Institut de Mathématiques de Marseille (I2M)
%A Neumann, Walter D
%A Pichon, Anne
%< avec comité de lecture
%@ 1949-2006
%J Journal of Singularities
%I Worldwide Center of Mathematics, LLC
%P 225-234
%8 2014
%D 2014
%R 10.5427/jsing.2014.10o
%K bilipschitz
%K Lipschitz geometry
%K complex curve singularity
%K embedded topological type.
%Z Mathematics [math]/Algebraic Geometry [math.AG]Journal articles
%X We describe the Lipschitz geometry of complex curves. To a large part this is well known material, but we give a stronger version even of known results. In particular, we give a quick proof, without any analytic restrictions, that the outer Lipschitz geometry of a germ of a complex plane curve determines and is determined by its embedded topology. This was first proved by Pham and Teissier, but in an analytic category. We also show the embedded topology of a plane curve determines its ambient Lipschitz geometry.
%G English
%L hal-01130555
%U https://hal.science/hal-01130555
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-