Current Developments in Mathematics

Volume 2013

Applications of Almgren-Pitts Min-max theory

Pages: 1 – 71

DOI: http://dx.doi.org/10.4310/CDM.2013.v2013.n1.a1

Authors

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

André Neves (Imperial College, London, United Kingdom)

Abstract

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.

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