论文标题
雅各布猜想的更强版本的最小值论点
A minimax argument to a stronger version of the Jacobian conjecture
论文作者
论文摘要
本文的主要结果是证明在对称假设下具有强大的真实雅各布猜想，并揭示了它与雅各布的猜想之间的联系。确切地说，我们假设$ f：\ mathbb {r}^n \ to \ mathbb {r}^n $是$ c^1 $地图，$ n \ geqslant 2 $，如果某些$ \ varepsilon> 0 $，$ 0 $，$ 0 （ - \ infty， - \ varepsilon）〜\ mbox {or}〜（\ varepsilon，+\ infty），其中$ spec（f）$表示$ jf $ and $ jf $ and $ jf $ and $ jf $ and $ jf+f+f^t的所有特征，$ spipe $ spemipe $ jf+jf+jf^t $ in Indect $ in Indift y in Indife in Indife in Indife in Indife in Indife in Indife。使用minimax参数证明了这一点。
The main result of this paper is to prove the strong real Jacobian conjecture under the symmetric assumption and reveals the link between it and the Jacobian conjecture. Precisely, we assume that $F: \mathbb{R}^n \to \mathbb{R}^n$ is of $C^1$ map, $n\geqslant 2$, if for some $\varepsilon >0$, $ 0\notin Spec(F)~~\mbox{and}~ Spec(F+F^T) \subseteq (-\infty,-\varepsilon)~\mbox{or} ~(\varepsilon,+\infty),$ where $Spec (F)$ denotes all eigenvalues of $JF$ and $Spec (F+F^T)$ denotes all eigenvalues of $JF+JF^T$, then we show that $F$ is injective. It is proved by using a minimax argument.
