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

Autor:	Sabatini, Marco
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs 14R15
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.05542 Zobrazit plný text záznamu View this record from Arxiv