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arXiv · 2404.17407

Interior regularity of area minimizing currents within a $C^{2,\alpha}$-submanifold

Stefano Nardulli·Reinaldo Resende
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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 $C^{2,\alpha}$.

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Stefano Nardulli, Reinaldo Resende. 2024-04-26. Interior regularity of area minimizing currents within a $C^{2,\alpha}$-submanifold. https://arxiv.org/abs/2404.17407

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