相关论文: Comment on a Paper by Yucai Su On Jacobian Conject…
The said paper [Su2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is false.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We show that the Jacobian conjecture of the two dimensional case is true.
We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.
We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
The said paper entitled "A Proof Of The Plane Jacobian Conjecture" is not true.
This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…
Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…
The two dimensional Jacobian Conjecture says that a morphism $f:\mathbb{C}[x,y]\to \mathbb{C}[x,y]$ having an invertible Jacobian, is invertible. We show that a morphism $f$ having an invertible Jacobian is invertible, in each of the…
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.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.
This paper has been withdrawn by the authors due to an error in Section 7.
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…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
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.
This is a Seminaire Bourbaki survey of the proof of the Kakeya conjecture in three dimensions. The survey is written for a broad mathematical audience. We sketch all the ideas in the proof, with many pictures.
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.