Applications of Almgren-Pitts Min-max theory

Fernando C. Marques, André Neves
2013 Current Developments in Mathematics  
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.
doi:10.4310/cdm.2013.v2013.n1.a1 fatcat:s2aogzj46zg43bjq2fv25q5csa