An Optimization Approach to Jacobian Conjecture

Jiang Liu

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arXiv · 2002.10249

An Optimization Approach to Jacobian Conjecture

Jiang Liu

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Abstract

Let $n\geq 2$ and $\mathbb K $ be a number field of characteristic $0$. Jacobian Conjecture asserts for a polynomial map $\mathcal P$ from $\mathbb K ^n$ to itself, if the determinant of its Jacobian matrix is a nonzero constant in $\mathbb K $ then the inverse $\mathcal P^{-1}$ exists and is also a polynomial map. This conjecture was firstly proposed by Keller in 1939 for $\mathbb K ^n=\mathbb C^2$ and put in Smale's 1998 list of Mathematical Problems for the Next Century. This study is going to present a proof for the conjecture. Our proof is based on Dru{\.{z}}kowski Map and Hadamard's Diffeomorphism Theorem, and additionally uses some optimization idea.

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Jiang Liu. 2020-02-19. An Optimization Approach to Jacobian Conjecture. https://arxiv.org/abs/2002.10249

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