Title | The fine structure of the singular set of area-minimizing integral currents III: Frequency 1 flat singular points and H^{m-2}-a.e uniqueness of tangent cones |
Publication Type | Journal Article |
Year of Publication | 2023 |
Authors | De Lellis C, Minter P, 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. We prove that T has a unique tangent cone, which is a superposition of planes, at Hm−2-a.e. point in its support. In combination with works of the first and third authors, we conclude that the singular set of T is countably (m−2)-rectifiable. The techniques in the present work can be seen as a counterpart for area-minimizers, in arbitrary codimension, to those developed by Simon ([29]) for multiplicity one classes of minimal surfaces and Wickramasekera ([32]) for stable minimal hypersurfaces. |
Notes | Preprint |
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