{"id":"openai-math/The-Solomon-Yau-least-volume-theorem","pdf":"https://github.com/openai/math/blob/main/preprints/The-Solomon-Yau-least-volume-theorem-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Solomon-Yau-least-volume-theorem-September-23-2026","tags":["differential-geometry","minimal-submanifolds","minimal-hypersurfaces"],"score":0,"title":"The Solomon–Yau least-volume theorem","domain":"Differential geometry","family":"349","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.20453","date":"2026-10-14","kind":"web","site":"arXiv.org","text":"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…","added":"2026-10-24","title":"Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equators","author":"Jingwen Chen","record":"arxiv/2610.20453"}],"formalized":false,"family_title":"The Solomon–Yau least-volume conjecture"}