Title | The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than 1 |
Publication Type | Journal Article |
Year of Publication | 2023 |
Authors | De Lellis C, Skorobogatova A |
Type of Article | Interior regularity |
Abstract | We consider an area-minimizing integral current T of codimension higher than 1 in a smooth Riemannian manifold Σ. In a previous paper we have subdivided the set of interior singular points with at least one flat tangent cone according to a real parameter, which we refer to as ``singularity degree''. This parameter determines the infinitesimal order of contact at the point in question between the ``singular part'' of T and its ``best regular approximation''. In this paper we show that the set of points for which the singularity degree is strictly larger than 1, is (m−2)-rectifiable. In a subsequent work we prove that the remaining flat singular points form an (m−2)-null set, thus concluding that the singular set of T is (m−2)-rectifiable. |
Notes | Accepted for publication in Comm. Math. Helvetici |
Order:
15