Lipschitz geometry of complex curves

Walter D Neumann and Anne Pichon

Journal of Singularities
volume 10 (2014), 225-234

Received 5 February 2013. Received in revised form 9 March 2014.

DOI: 10.5427/jsing.2014.10o

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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.


bilipschitz, Lipschitz geometry, complex curve singularity, embedded topological type

Mathematical Subject Classification:

14B05, 32S25, 32S05, 57M99

Author(s) information:

Walter D Neumann Anne Pichon
Department of Mathematics Aix Marseille Université, CNRS
Barnard College, Columbia University Centrale Marseille
2009 Broadway MC4424 I2M, UMR 7373
New York, NY 10027, USA 13453 Marseille, FRANCE
email: email: