Current Developments in Mathematics

Volume 2013

Applications of Almgren-Pitts Min-max theory

Pages: 1 – 71



Fernando C. Marques (Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil)

André Neves (Imperial College, London, United Kingdom)


We survey recent applications of Almgren-Pitts Min-max theory found by the authors. Namely, the proof of the Willmore conjecture, the proof of the Freedman-He-Wang conjecture on the Möbius energy of links (jointly with Ian Agol), and the proof that manifolds with positive Ricci curvature metrics admit an infinite number of minimal hypersurfaces.

Published 22 October 2014