Current Developments in Mathematics
Applications of Almgren-Pitts Min-max theory
Pages: 1 – 71
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.