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preprint · arXiv (Cornell University) · 2022

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

Marco Sabatini

Cited by 0Open access

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.

Cite this paper

APA 7

Sabatini, M. (2022). Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2202.05542

MLA 9

Sabatini, Marco. “Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space.” arXiv (Cornell University), 2022, https://doi.org/10.48550/arxiv.2202.05542.

Chicago

Sabatini, Marco. 2022. “Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2202.05542.

Harvard

Sabatini, M. (2022) ‘Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2202.05542.

BibTeX
@misc{sabatini2022injectivity,
  title = {{Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space}},
  author = {Sabatini, Marco},
  journal = {arXiv (Cornell University)},
  year = {2022},
  doi = {10.48550/arxiv.2202.05542}
}

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