An Optimization Approach to Jacobian Conjecture

Abstract

Let $n\ge 2$ 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{ż}kowski Map and Hadamard's Diffeomorphism Theorem, and additionally uses some optimization idea.

A research article about Jacobian Conjecture in Math

References in corpus (2)

• A note on the Jacobian Conjecture
• Some observations on the properness of identity plus linear powers: part 2

Cited by in corpus (1)

• Some observations on the properness of identity plus linear powers: part 2