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Global injectivity and real Jacobian conjecture in ℝn

  • Xinhao Hu
  • Jaume Llibre
  • Yilei Tang
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Abstract

In this paper, we study the global injectivity of local diffeomorphisms in ℝn, extending the criterions of Braun and Llibre in [{\it Pacific J. Math.} {\bf 333} (2024) 1--15] from the planar radial case to arbitrary dimension. Then we extend the results of Llibre and Mello in [{\it Bull. Sci. Math.} {\bf 213} (2026) 103889] to arbitrary dimension, obtaining two necessary and sufficient conditions for the real Jacobian conjecture in ℝn by qualitative theory of differential equations. Finally, using weighted Poincaré compactification in ℝn, we provide a sufficient condition for the real Jacobian conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026global,
  title = {{Global injectivity and real Jacobian conjecture in $\mathbbR^n$}},
  author = {Xinhao Hu and Jaume Llibre and Yilei Tang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32391},
  eprint = {2610.32391},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32391},
}
RIS
TY  - UNPB
TI  - Global injectivity and real Jacobian conjecture in ℝ^n
AU  - Xinhao Hu
AU  - Jaume Llibre
AU  - Yilei Tang
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32391
UR  - https://arxiv.org/abs/2610.32391
AB  - In this paper, we study the global injectivity of local diffeomorphisms in ℝ^n, extending the criterions of Braun and Llibre in [{\it Pacific J. Math.} {\bf 333} (2024) 1--15] from the planar radial case to arbitrary dimension. Then we extend the results of Llibre and Mello in [{\it Bull. Sci. Math.} {\bf 213} (2026) 103889] to arbitrary dimension, obtaining two necessary and sufficient conditions for the real Jacobian conjecture in ℝ^n by qualitative theory of differential equations. Finally, using weighted Poincaré compactification in ℝ^n, we provide a sufficient condition for the real Jacobian conjecture.
ER  -