Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equators
Jingwen Chen
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.
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