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16 papers · 1 filter
A characterization of Lipschitz normally embedded surface singularities
Walter D Neumann, Helge Møller Pedersen, Anne Pichon
Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the…
Lipschitz geometry does not determine embedded topological type
Walter D. Neumann, Anne Pichon
We investigate the relationships between the Lipschitz outer geometry and the embedded topological type of a hypersurface germ in . It is well known that the Lipsc…
Minimal surface singularities are Lipschitz normally embedded
Walter D Neumann, Helge Møller Pedersen, Anne Pichon
Any germ of a complex analytic space is equipped with two natural metrics: the {\it outer metric} induced by the hermitian metric of the ambient space and the {\it inner metric}, w…
The thick-thin decomposition and the bilipschitz classification of normal surface singularities
Lev Birbrair, Walter D Neumann, Anne Pichon
We describe a natural decomposition of a normal complex surface singularity into its "thick" and "thin" parts. The former is essentially metrically conical, while the latte…
Separating sets, metric tangent cone and applications for complex algebraic germs
Lev Birbrair, Alexandre Fernandes, Walter D Neumann
An explanation is given for the initially surprising ubiquity of separating sets in normal complex surface germs. It is shown that they are quite common in higher dimensions too. T…
mu-constancy does not imply constant bi-Lipschitz type
Lev Birbrair, Alexandre Fernandes, Walter Neumann
We show that a family of isolated complex hypersurface singularities with constant Milnor number may fail, in the strongest sense, to have constant bi-Lipschitz type. Our example i…