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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
29/2003

The min--max construction of minimal surfaces

Tobias H. Colding and Camillo De Lellis

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.

Received:
25.03.03
Published:
25.03.03
MSC Codes:
49Q05, 53A10, 49Q15
Keywords:
min--max, minimal submanifolds, varifolds

Related publications

inBook
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)