Almgren's type regularity for Semicalibrated Currents

Abstract

In analogy with Almgren's Theorem for area minimizing currents of general dimension and codimension, we prove that an $m$-dimensional semicalibrated current in a $(n+m)$-dimensional $C^{3,{\epsilon }_0}$ manifold, semicalibrated by a $C^{2,{\epsilon }_0}$ $m$-form, has singular set of Hausdorff dimension at most $m-2$.

arXiv commentExpanded introduction, some typos corrected. arXiv admin note: text overlap with arXiv:1508.05509