The Solomon–Yau least-volume conjecture. 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.
released 2026-09-23 | 3 theorems · 19 lemmas · 27 proofs · 14,312 words |
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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.