Surveys in Differential Geometry

Volume 21 (2016)

Topology of the space of cycles and existence of minimal varieties

Pages: 165 – 177

DOI: https://dx.doi.org/10.4310/SDG.2016.v21.n1.a5

Authors

Fernando C. Marques (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)

André Neves (Imperial College, London, United Kingdom)

Abstract

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.

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Published 7 June 2016