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Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equators
Abstract
In this short note, using OpenAI's resolution of the Solomon--Yau conjecture, we extend our joint work with Pedro Gaspar to all dimensions n≥2. We construct eternal Allen--Cahn flows on Sn+1 connecting approximations of any prescribed least-area Clifford hypersurface and equatorial sphere. We also construct infinitely many eternal integral Brakke flows from least-area Clifford hypersurfaces to equatorial spheres.
Related
- Finite-Shift Inverse-Concavity and Exterior Noncollapsing for Fully Nonlinear Curvature Flows of Nonconvex Hypersurfaces
- Multiplicity One for Strictly Stable Anisotropic Allen-Cahn Minimal Hypersurfaces
- Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow
- Biharmonic Conformal Immersions of Hypersurfaces: Dirac Rigidity and Mixed Clifford Geometry
- A Second-Order Maximum-Bound-Preserving and Energy-Stable Exponential Time-Differencing Method for Allen--Cahn-Type Gradient Flows
BibTeX
@misc{chen2026allencahn,
title = {{Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equators}},
author = {Jingwen Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20453},
eprint = {2610.20453},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20453},
}
RIS
TY - UNPB
TI - Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equators
AU - Jingwen Chen
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20453
UR - https://arxiv.org/abs/2610.20453
AB - In this short note, using OpenAI's resolution of the Solomon--Yau conjecture, we extend our joint work with Pedro Gaspar to all dimensions n≥2. We construct eternal Allen--Cahn flows on S^n+1 connecting approximations of any prescribed least-area Clifford hypersurface and equatorial sphere. We also construct infinitely many eternal integral Brakke flows from least-area Clifford hypersurfaces to equatorial spheres.
ER -