On the origin of the Gibbons conjecture

Renan J. S. Isneri

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arXiv · 2605.29848

On the origin of the Gibbons conjecture

Renan J. S. Isneri

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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.

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Renan J. S. Isneri. 2026-05-28. On the origin of the Gibbons conjecture. https://arxiv.org/abs/2605.29848

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