The Willmore Conjecture

Fernando C. Marques, André Neves

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing together ideas from subjects like conformal geometry, partial differential equations, algebraic geometry and geometric measure theory. In this article we survey the history of the conjecture and our recent solution through the min-max approach. We finish with a discussion of some of the many open questions that remain in the field.

Original languageEnglish (US)
Pages (from-to)201-222
Number of pages22
JournalJahresbericht der Deutschen Mathematiker-Vereinigung
Issue number4
StatePublished - Dec 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Bending energy
  • Min-max theory
  • Minimal surfaces
  • Willmore surfaces


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