The Solomon–Yau least-volume theorem
We prove the Solomon–Yau least-volume conjecture for minimal hypersurfaces of unit round spheres: in every dimension m ≥ 2, a closed connected minimal immersion with non-totally-geodesic image has volume at least the smallest m -dimensional minimal Clifford product. Volume is measured on the domain, so covering multiplicities are included.
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Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equatorsarXiv.orgJingwen ChenOct 14, 2026in the index
In this short note, using OpenAI's resolution of the Solomon--Yau conjecture, we extend our joint work with Pedro Gaspar to all dimensions $n\geq2$. We construct eternal Allen--Cahn flows on $S^{n+1}$ connecting approximations of any prescribed least-area Clifford hypersurface and equatorial…