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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In The Solomon–Yau least-volume theorem, 23 September 2026
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Let m\ge2, let M^m be a closed connected smooth manifold, and let F:M\to S^{m+1} be a smooth minimal immersion into the unit round sphere. If F(M) is not totally geodesic, then
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Theorem 1.1
In The Solomon–Yau least-volume theorem, 23 September 2026