On Gronwall conjecture
Differential Geometry
2014-07-14 v2
Abstract
Gronwall conjecture states that a planar 3-web which admits more than one distinct linearization is locally equivalent to an algebraic web. We give a partial answer to the conjecture in the affirmative for the class of planar 3-webs with the web curvature that vanishes to order three at a point. The differential relation on the third order jet of web curvature provides an explicit criterion for unique linearization.
Keywords
Cite
@article{arxiv.1102.0066,
title = {On Gronwall conjecture},
author = {Joe S. Wang},
journal= {arXiv preprint arXiv:1102.0066},
year = {2014}
}
Comments
26 pages, to appear in Journal of Geometric Analysis. Note: The main result of the Vaona's paper "Sul teorema fondamentale della nomografia" quoted in the introduction does not appear to hold as it stands. The set of four equations on page 262 are linearly dependent