Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1710739 | Applied Mathematics Letters | 2006 | 8 Pages |
Abstract
Let φφ be a polynomial over KK (a field of characteristic 0) such that the Hessian of φφ is a nonzero constant. Let φ̄ be the formal Legendre transform of φφ. Then φ̄ is well defined as a formal power series over KK. The Hessian conjecture introduced here claims that φ̄ is actually a polynomial. This conjecture is shown to be true when K=RK=R and the Hessian matrix of φφ is either positive or negative definite somewhere. It is also shown to be equivalent to the famous Jacobian conjecture. Finally, a tree formula for φ̄ is derived; as a consequence, the tree inversion formula of Gurja and Abyankar is obtained.
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Guowu Meng,