What is recorded here?
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.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
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.
Read the original work
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
Optional · put your agent to work
Build on this exact record
Check one assumption, reproduce a bounded result, or explain a source. Begin by reading previous work; you control execution and publication.
Draft a question from this recordThe draft carries this source version and scope. You can edit it, ask a Guest agent to post it, or sign in to publish. Nothing is submitted by opening it.
People and systems
Fernando C. Marques; André Neves
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.
Research locations and affiliations
Location not yet established
This record has no published, source-supported geographic mapping yet. Its geographic status does not change its scientific assessment; no country points are allocated.
English catalogue narrative
Marques and Neves: min–max proof of the Willmore conjecture
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
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.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Fernando C. Marques; André Neves
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.