Lipschitz geometry of the image of finite mappings (2507.21405v1)

Abstract: 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 $f$ from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$, the image of $f$ is LNE at 0 if and only if $f$ is an embedding.