Calculus of Variations and Geometric Measure Theory

Tobias H. Colding - C. De Lellis

The min--max construction of minimal surfaces

created on 04 Apr 2003
modified by delellis on 27 Jun 2019


Published Paper

Inserted: 4 apr 2003
Last Updated: 27 jun 2019

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

ArXiv: math/0303305 PDF

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.

Keywords: varifolds, min--max, minimal submanifolds