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Mathematics > Analysis of PDEs
Title: Interior regularity of area minimizing currents within a $C^{2,α}$-submanifold
(Submitted on 26 Apr 2024)
Abstract: Given an area-minimizing integral $m$-current in $\Sigma$, we prove that the Hausdorff dimension of the interior singular set of $T$ cannot exceed $m-2$, provided that $\Sigma$ is an embedded $(m+\bar{n})$-submanifold of $\mathbb{R}^{m+n}$ of class $C^{2,\alpha}$, where $\alpha>0$. This result establishes the complete counterpart, in the arbitrary codimension setting, of the interior regularity theory for area-minimizing integral hypercurrents within a Riemannian manifold of class $C^{2,\alpha}$.
Submission history
From: Reinaldo Resende [view email][v1] Fri, 26 Apr 2024 13:35:58 GMT (1247kb,D)
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