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arXiv · 2507.21405

Lipschitz geometry of the image of finite mappings

Juan José Nuño Ballesteros·Vinícius de Oliveira Prado·Guillermo Peñafort Sanchis·José Edson Sampaio
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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.

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Juan José Nuño Ballesteros, Vinícius de Oliveira Prado, Guillermo Peñafort Sanchis, José Edson Sampaio. 2025-07-29. Lipschitz geometry of the image of finite mappings. https://arxiv.org/abs/2507.21405

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