Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space
DOI:
https://doi.org/10.12775/TMNA.2022.073Keywords
Jacobian conjecture, global injectivity, eigenvalue continuityAbstract
Fessler and Gutierrez \cite{Fe}, \cite{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 $\partial P/\partial x + \partial Q/\partial y$ is not a surjective function.References
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