Homemath.HOarXiv:2605.29848

On the origin of the Gibbons conjecture

math.HOmath.AP2026-05v1license

Abstract

The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a 1995 paper by Carbou and to subsequent developments in the literature. We argue that the attribution likely arose from informal communication rather than from a formally stated conjecture, illustrating how mathematical terminology may develop through transmission and collective usage.

Cite

@article{arxiv.2605.29848,
  title  = {On the origin of the Gibbons conjecture},
  author = {Renan J. S. Isneri},
  journal= {arXiv preprint arXiv:2605.29848},
  year   = {2026}
}