Surveys in Differential Geometry
Volume 21 (2016)
Topology of the space of cycles and existence of minimal varieties
Pages: 165 – 177
In this article we survey what is known about the existence of minimal varieties of dimension $l \geq 2$ in compact Riemannian manifolds. We describe how min-max methods can be used in conjunction with the nontrivial topology of the space of cycles. In the final section, we propose some open questions in the subject.