SWhat changed
A canonical five-parameter family and Almgren–Pitts min–max methods prove the 2π² Willmore-energy lower bound for embedded closed positive-genus surfaces in the round three-sphere, with conformal Clifford-torus equality. The source explains how the Euclidean immersed-torus conjecture follows using existing nonembedded-surface bounds.
Scientific scope
A canonical five-parameter family and Almgren–Pitts min–max methods prove the 2π² Willmore-energy lower bound for embedded closed positive-genus surfaces in the round three-sphere, with conformal Clifford-torus equality. The source explains how the Euclidean immersed-torus conjecture follows using existing nonembedded-surface bounds. The geometric setting, mean-curvature normalization, genus and embedding assumptions belong to the stated theorem. The immersed extension uses inherited Li–Yau results. This entry records the geometric theorem and its stated inherited implications.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The geometric setting, mean-curvature normalization, genus and embedding assumptions belong to the stated theorem. The immersed extension uses inherited Li–Yau results. This entry records the geometric theorem and its stated inherited implications.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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