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 M can be approximated in flat norm by an integral cycle in the same homology class which is a smooth submanifold Σ of nearly the same area, up to a singular set of codimension 5. Moreover, if the homology class τ is representable by a smooth submanifold, then Σ can be chosen free of singularities.

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14