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arXiv · 1906.11545

A step to Gronwall's conjecture

Jean Paul Dufour
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Abstract

In this paper we will explore a way to prove the hundred years old Gronwall's conjecture: if two plane linear 3-webs with non-zero curvature are locally isomorphic, then the isomorphism is a homography. Using recent results of S. I. Agafonov, we exhibit an invariant, the {\sl characteristic}, attached to each generic point of such a web, with the following property: if a diffeomorphism interchanges two such linear webs, sending a point of the first to a point of the second which have the same characteristic, then this diffeomomorphism is locally a homography.

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Jean Paul Dufour. 2019-06-27. A step to Gronwall's conjecture. https://arxiv.org/abs/1906.11545

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