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arXiv · 1603.07543

Foliations, solvability and global injectivity

Francisco Braun·José Ruidival dos Santos Filho·Marco Antonio Teixeira
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Abstract

Let $F: \mathbb{R}^n\to\mathbb{R}^n$ be a $C^{\infty}$ map such that $DF(x)$ is invertible for every $x\in\mathbb{R}^n$. Although being a local diffeomorphism, $F$ is not necessarily globally injective if $n\geq2$. Finding additional assumptions implying the global injectivity of $F$ for $n\geq 2$ is object of intense study in several areas of Mathematics. In this paper we revisit some assumptions and relations between them in the bidimensional case and discuss the natural higher dimensional situation.

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Francisco Braun, José Ruidival dos Santos Filho, Marco Antonio Teixeira. 2016-03-24. Foliations, solvability and global injectivity. https://doi.org/10.1007/s00013-022-01789-z

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