Differential geometry·OpenAI Math·Result 349
The Solomon–Yau least-volume conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under differential geometry: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
The Solomon–Yau least-volume theorem
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What OpenAI claims
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 Sm+1 with non-totally-geodesic image has volume at least that of the smallest minimal Clifford product, counting covering multiplicity.
Paper
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.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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