∑math20

Differential geometry · Result 349

The Solomon–Yau least-volume conjecture

1 paper

Proves the Solomon–Yau least-volume conjecture for minimal hypersurfaces of round spheres. For every m ≥ 2, a closed connected minimal immersion into the unit sphere \(S^{m+1}\) with non-totally-geodesic image has volume at least that of the smallest minimal Clifford product, counting covering multiplicity.

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Papers 1

First page of The Solomon–Yau least-volume theorem

The Solomon–Yau least-volume theorem

OpenAI · September 23, 2026

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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@misc{OAI:The-Solomon-Yau-least-volume-theorem-September-23-2026,
  author = {{OpenAI}},
  title = {{The Solomon--Yau least-volume theorem}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Solomon-Yau-least-volume-theorem-September-23-2026/paper.pdf}{OAI:The-Solomon-Yau-least-volume-theorem-September-23-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.