New proofs for the Abhyankar-Gurjar inversion formula and the equivalence of the Jacobian conjecture and the vanishing conjecture-Reference-Cited by-同舟云学术

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

Published:2011-01-26 Issue:9 Volume:139 Page:3141-3154
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Zhao Wenhua

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2011-139-09/S0002-9939-2011-10744-5/S0002-9939-2011-10744-5.pdf

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5. A reduction of the Jacobian conjecture to the symmetric case;de Bondt, Michiel;Proc. Amer. Math. Soc.,2005

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