TitleOptimal smooth approximation of integral cycles
Publication TypeJournal Article
Year of Publication2024
AuthorsAlmgren F, Browder W, Caldini G, De Lellis C
Type of Articlegeometric measure theory
Abstract

In this article we prove that each integral cycle $T$ in an oriented Riemannian manifold $\mathcal{M}$ can be approximated in flat norm by an integral cycle in the same homology class which is a smooth submanifold $\Sigma$ of nearly the same area, up to a singular set of codimension 5. Moreover, if the homology class $\tau$ is representable by a smooth submanifold, then $\Sigma$ can be chosen free of singularities.

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