English

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

R2 v1 2026-06-21T17:19:46.283Z