Browsing Singularity Theory and Algebraic Geometry by Author "Fernandes, A."
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Hölder equivalence of complex analytic curve singularities
Fernandes, A.; Sampaio, J.E.; Silva, J.P. (20180806)We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$H\"older ... 
Multiplicity and degree as bi‐Lipschitz invariants for complex sets
Fernandes, A.; Fernández de Bobadilla, J.; Sampaio, J.E. (20180829)We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer biLipschitz transformations (outer biLipschitz homeomorphims of germs in the first case and outer biLipschitz ... 
Multiplicity of singularities is not a biLipschitz invariant
Birbrair, L.; Fernandes, A.; Sampaio, J.E.; Verbitsky, M. (20200117)It was conjectured that multiplicity of a singularity is biLipschitz invariant. We disprove this conjecture constructing examples of biLipschitz equivalent complex algebraic singularities with different values of multiplicity. 
On Lipschitz rigidity of complex analytic sets
Fernandes, A.; Sampaio, J.E. (20190226)We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of ...