Related papers: The Dimension Conjecture Implies The Jacobi Bound …

We show that the Jacobian conjecture of the two dimensional case is true.

We prove the Strong Jacobi Bound Conjecture for generically reduced components of differential schemes.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…

We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-example to a more general statement known as the Moments Vanishing…

We prove the Jacobian Conjecture for the space of all the inner functions in the unit disc.

A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered

We prove the Aharoni Berger Conjecture

We prove that the Jacobian conjecture is false if and only if there exists a solution to a certain system of polynomial equations. We analyse the solution set of this system. In particular we prove that it is zero dimensional.

One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.

We prove a conjecture due to Y. Last on Jacobi matrices.

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

Using the author's inversion formula for automorphisms of the Weyl algebras with polynomial coefficients and the bound on its degree a slightly shorter (algebraic) proof is given of the result of A. Belov-Kanel and M. Kontsevich that the…

We investigate the 2-dimensional jacobian conjecture via Klein's program.

The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of the Image Conjecture and show how it leads to…

The Jacobian conjecture in dimension $n$ asserts that any polynomial endomorphism of $n$-dimensional affine space over a field of zero characteristic, with the Jacobian equal 1, is invertible. The Dixmier conjecture in rank $n$ asserts that…

Let $F:\mathbb{C}[x_1,\ldots,x_n] \to \mathbb{C}[x_1,\ldots,x_n]$ be a $\mathbb{C}$-algebra endomorphism that has an invertible Jacobian. We bring two ideas concerning the Jacobian Conjecture: First, we conjecture that for all $n$, the…