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Almgren–Pitts min-max theory Teoria de Almgren-Pitts
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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. Em matemática, a teoria de Almgren-Pitts (nomeada após Frederick J. Almgren, Jr. e seu aluno Jon T. Pitts), também chamada teoria min-max das superfícies mínimas é uma teoria de hipersuperfícies análoga à (que se aplica a variedades). A teoria desempenhou papéis nas soluções para várias conjecturas em geometria e topologia pelos próprios F. Almgren e J. Pitts e também por M. L. Gromov, R. Schoen, S.-T. Yau, F. C. Marques, A. A. Neves, I. Agol, dentre outros.
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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. Em matemática, a teoria de Almgren-Pitts (nomeada após Frederick J. Almgren, Jr. e seu aluno Jon T. Pitts), também chamada teoria min-max das superfícies mínimas é uma teoria de hipersuperfícies análoga à (que se aplica a variedades). A teoria desempenhou papéis nas soluções para várias conjecturas em geometria e topologia pelos próprios F. Almgren e J. Pitts e também por M. L. Gromov, R. Schoen, S.-T. Yau, F. C. Marques, A. A. Neves, I. Agol, dentre outros.
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