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arXiv · 1902.03615

A minimax principle to the injectivity of the Jacobian conjecture

Wei Liu·Quan Xu
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Abstract

The main result of this paper is to prove some type of Real Jacobian Conjecture. It is proved by the Minimax Principle and asserts if the eigenvalues of $F'(x)$ are bounded from zero and all the eigenvalues of $F'(x)+F'(x)^T$ are strictly same sign, where $ F $ is $ C^1 $ mapping from $ \mathbb{R}^n $ to $ \mathbb{R}^n $, then $ F $ is injective. Moreover $F$ has a $ C^1 $ mapping inverse.

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BibTeXRIS

Wei Liu, Quan Xu. 2019-02-10. A minimax principle to the injectivity of the Jacobian conjecture. https://arxiv.org/abs/1902.03615

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