%0 Unpublished work
%T Lipschitz geometry of complex surfaces: analytic invariants and equisingularity
%+ Columbia University [New York]
%+ Institut de Mathématiques de Marseille (I2M)
%A Neumann, Walter D
%A Pichon, Anne
%8 2012-11-20
%D 2012
%K normal surface singularity
%K Lipschitz geometry
%K bilipschitz
%K Zariski equisingularity
%K Lipschitz equisingularity.
%Z Mathematics [math]/Algebraic Geometry [math.AG]Preprints, Working Papers, ...
%X We prove that the outer Lipschitz geometry of the germ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities with constant Lipschitz geometry is Zariski equisingular. We also prove a strong converse for families of normal complex hypersurface singularities in $\C^3$: Zariski equisingularity implies Lipschitz triviality. So for such a family Lipschitz triviality, constant Lipschitz geometry and Zariski equisingularity are equivalent to each other.
%G English
%2 https://hal.science/hal-01130560/document
%2 https://hal.science/hal-01130560/file/1211.4897v2.pdf
%L hal-01130560
%U https://hal.science/hal-01130560
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-