OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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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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MANUSCRIPT 01
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…
Full source abstract
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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