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 $n\ge 2$. 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.

arXiv comment9 pages, comments are welcome!