Now showing items 1-4 of 4

• #### Hölder equivalence of complex analytic curve singularities ﻿

(2018-08-06)
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 ﻿

(2018-08-29)
We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz ...
• #### Multiplicity of singularities is not a bi-Lipschitz invariant ﻿

(2020-01-17)
It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.
• #### On Lipschitz rigidity of complex analytic sets ﻿

(2019-02-26)
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 ...