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arXiv · 2110.01051

Surjectivity of linear operators and semialgebraic global diffeomorphisms

Francisco Braun·Luis Renato Gonçalves Dias·Jean Venato Santos
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Abstract

We prove that a $C^{\infty}$ semialgebraic local diffeomorphism of $\mathbb{R}^n$ with non-properness set having codimension greater than or equal to $2$ is a global diffeomorphism if $n-1$ suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of $\mathbb{R}^n$. Our conjecture implies a very known conjecture of Z. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature.

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Francisco Braun, Luis Renato Gonçalves Dias, Jean Venato Santos. 2021-10-03. Surjectivity of linear operators and semialgebraic global diffeomorphisms. https://doi.org/10.1007/s11854-023-0286-z

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