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1. CJM 2002 (vol 54 pp. 1187)
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On the Injectivity of $C^1$ Maps of the Real Plane Let $X\colon\mathbb{R}^2\to\mathbb{R}^2$ be a $C^1$ map. Denote by $\Spec(X)$ the set of
(complex) eigenvalues of $\DX_p$ when $p$ varies in $\mathbb{R}^2$. If there exists
$\epsilon >0$ such that $\Spec(X)\cap(-\epsilon,\epsilon)=\emptyset$, then
$X$ is injective. Some applications of this result to the real Keller Jacobian
conjecture are discussed.
Categories:34D05, 54H20, 58F10, 58F21 |