Min-Max theory and the Willmore conjecture

Fernando C. Marques, André Neves

Research output: Contribution to journalArticle

132 Scopus citations


In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R3 is at least 2π2. We prove this conjecture using the min-max theory of minimal surfaces.

Original languageEnglish (US)
Pages (from-to)683-782
Number of pages100
JournalAnnals of Mathematics
Issue number2
StatePublished - Mar 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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