The min--max construction of minimal surfaces

Tobias H. Colding and Camillo De Lellis

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Submission date: 25. Mar. 2003
Pages: 35
published in: Lectures on geometry and topology : lectures on geometry and topology held in honor of Calabi, Lawson, Siu, and Uhlenbeck / S.-T. Yau ... (eds.)
Somerville, MA : Internat. Press, 2003. - P. 75 - 107
(Surveys in differential geometry ; 8) 
DOI number (of the published article): 10.4310/SDG.2003.v8.n1.a3
Bibtex
MSC-Numbers: 49Q05, 53A10, 49Q15
Keywords and phrases: min--max, minimal submanifolds, varifolds
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Abstract:
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.