On this page
Spherical minimal-surface volume reference
Family 349: The Solomon–Yau least-volume conjecture. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Geometric optimization researchers can compare non-totally-geodesic closed minimal immersions against the Clifford-product volume lower bound.
Applicability and commercial boundary
Covering multiplicity, minimality and round-sphere setting matter; the result is not a generic finite membrane optimizer.
Initial business decision
Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.
Next verification action
Extract exact Clifford volumes and a separately justified minimality check.
Evidence scope
The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.