Tootfinder

Lipschitz geometry of the image of finite mappings
Juan Jos\'e Nu\~no Ballesteros, Vin\'icius de Oliveira Prado, Guillermo Pe\~nafort Sanchis, Jos\'e Edson Sampaio
https://arxiv.org/abs/2507.21405

Lipschitz geometry of the image of finite mappings
This paper is devoted to the study of the LNE property in complex analytic hypersurface parametrized germs, that is, the sets that are images of finite analytic map germs from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. We prove that if the multiplicity of $f$ is equal to his generic degree, then the image of $f$ is LNE at 0 if and only if it is a smooth germ. We also show that every finite corank 1 map is sattisfies the previous hypothesis. Moreover, we show that for an injective map germ $f…