Almgren–Pitts min-max theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-29

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Almgren%E2%80%93Pitts_min-max_theory


00:00:45 1 Description and basic concepts
00:01:03 2 See also



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SUMMARY
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In mathematics, the Almgren–Pitts min-max theory (named after Frederick J. Almgren, Jr. and his student Jon T. Pitts) 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.