Title | Optimal smooth approximation of integral cycles |
Publication Type | Journal Article |
Year of Publication | 2024 |
Authors | Almgren F, Browder W, Caldini G, De Lellis C |
Type of Article | geometric 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. |
Notes | Preprint |
Order:
14