Almgren–Pitts min-max theory
In mathematics, the Almgren–Pitts min-max theory is an analogue of Morse theory for hypersurfaces.
The theory started with the efforts for generalizing George David Birkhoff's method for the construction of simple closed geodesics on the sphere, to allow the construction of embedded minimal surfaces in arbitrary 3-manifolds.
It has played roles in the solutions to a number of conjectures in geometry and topology found by Almgren and Pitts themselves and also by other mathematicians, such as Mikhail Gromov, Richard Schoen, Shing-Tung Yau, Fernando Codá Marques, André Neves, Ian Agol, among others.Description and basic concepts
The theory allows the construction of embedded minimal hypersurfaces though variational methods.
