Calculus of Variations and Geometric Measure Theory
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T. Colding - C. De Lellis

The min--max construction of minimal surfaces

created on 04 Apr 2003
modified by delellis on 03 May 2011


Published Paper

Inserted: 4 apr 2003
Last Updated: 3 may 2011

Journal: Surveys in differential geometry
Volume: 8
Pages: 75-107
Year: 2003

Lectures on Geometry and Topology held in honor of Calabi, Lawson, Siu and Uhlenbeck at Harvard University, May 3--5, 2002


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.

For the most updated version and eventual errata see the page


Keywords: varifolds, min--max, minimal submanifolds

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