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arXiv · 2202.05542

Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space

Marco Sabatini
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Abstract

Fessler and Gutierrez \cite{Fe,Gu} proved that if a non-singular planar map has Jacobian matrix without eigenvalues in $(0,+\infty)$, then it is injective. We prove that the same holds replacing $(0,+\infty)$ with any unbounded curve disconnecting the upper (lower) complex half-plane. Additionally we prove that a Jacobian map $(P,Q)$ is injective if $P_x + Q_y$ is not a surjective function.

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Marco Sabatini. 2022-02-11. Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space. https://arxiv.org/abs/2202.05542

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