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The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $\mathcal{H}^{m-2}$-a.e. Uniqueness of Tangent Cones
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abstract
We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $\Sigma$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-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.
Forward citations
Cited by 4 Pith papers
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At almost every branch point with planar frequency ≠ 2, an area-minimizing current has a unique algebraic tangent blow-up, a higher-order expansion with remainder bounds, a locally rectifiable branch-set decomposition...
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