In this paper we give an overview of some aspects of the min-max theory of minimal surfaces, and discuss recent applications to conformally invariant problems in Geometry and Topology. The goal is to explain what the proofs of the Willmore conjecture for surfaces and the Freedman-He-Wang conjecture for links share in common. This is based on joint work of the authors  and on joint work of I. Agol and the authors .
All Science Journal Classification (ASJC) codes
- conformal geometry
- links in space
- min-max method
- minimal surfaces