4 papers
On metric equivalence of the Brieskorn-Pham hypersurfaces
Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at . Moreover we show that if two algebraic -dimensional cones $P, R\su…
Hölder invariance of the Henry-Parusinski invariant
Alexandre Fernandes, José Edson Sampaio, Joserlan Perote da Silva
In this article, we show the Hölder invariance of the Henry-Parusinski invariant. For a single germ , the Henry-Parusinski invariant of is given in terms of the leading c…
Bi-Lipschitz equivalent cones with different degrees
Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
We show that for every there exist complex algebraic cones of dimension with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they…
The multiplicity mod 2 is not a bi-lipschitz invariant
A. Fernandes, Z. Jelonek, J. E. Sampaio
We show that subanalytic bi-Lipschitz homeomorphisms in general does not preserve the multiplicities of real analytic sets.