On the origin of the Gibbons conjecture
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918529452736512 |
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| author | Isneri, Renan J. S. |
| author_facet | Isneri, Renan J. S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29848 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the origin of the Gibbons conjecture Isneri, Renan J. S. History and Overview Analysis of PDEs 01A60, 01A65, 35B06 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. |
| title | On the origin of the Gibbons conjecture |
| topic | History and Overview Analysis of PDEs 01A60, 01A65, 35B06 |
| url | https://arxiv.org/abs/2605.29848 |