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MiS Preprint

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.

MSC Codes:
49Q05, 53A10, 49Q15
min--max, minimal submanifolds, varifolds

Related publications

2003 Repository Open Access
Tobias H. Colding and Camillo De Lellis

The min-max construction of minimal surfaces

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)