New proofs for the Abhyankar-Gurjar inversion formula and the equivalence of the Jacobian conjecture and the vanishing conjecture

Zhao, Wenhua

doi:10.1090/S0002-9939-2011-10744-5

New proofs for the Abhyankar-Gurjar inversion formula and the equivalence of the Jacobian conjecture and the vanishing conjecture
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Proc. Amer. Math. Soc. 139 (2011), 3141-3154 Request permission

Abstract:

We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar formula to give a more straightforward proof for the equivalence of the Jacobian conjecture with a special case of the vanishing conjecture of (homogeneous) quadratic differential operators with constant coefficients.

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