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The min--max construction of minimal surfaces
Tobias H. Colding and Camillo De Lellis
In this paper we survey with complete proofs some well--known, but hard to find, results about constructing closed embedded minimal surfaces in a closed $3$-dimensional manifold via min--max arguments. This includes results of J. Pitts, F. Smith, and L. Simon and F. Smith.
In: Lectures on geometry and topology : lectures on geometry and topology held in honor of Calabi, Lawson, Siu, and Uhlenbeck / Shing-Tung Yau... (eds.) Somerville, MA : Internat. Press, 2003. - pp. 75-107 (Surveys in differential geometry ; 8)