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.
Published 13 January 2022