Stable solutions of the Allen--Cahn equation in dimension three are one-dimensional

@misc{chan2026stable,
  title = {{Stable solutions of the Allen--Cahn equation in dimension three are one-dimensional}},
  author = {Hardy Chan and Xavier Fernández-Real and Alessio Figalli and Enric Florit-Simon and Joaquim Serra},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30194},
  eprint = {2609.30194},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30194},
}

TY  - UNPB
TI  - Stable solutions of the Allen--Cahn equation in dimension three are one-dimensional
AU  - Hardy Chan
AU  - Xavier Fernández-Real
AU  - Alessio Figalli
AU  - Enric Florit-Simon
AU  - Joaquim Serra
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30194
UR  - https://arxiv.org/abs/2609.30194
AB  - We prove that every bounded stable solution of the Allen--Cahn equation in ℝ^3 is one-dimensional. As a consequence, this shows the validity of De Giorgi's conjecture for monotone solutions in dimension four.
ER  -