Calculus of Variations and Geometric Measure Theory

L. Spolaor

Almgren's type regularity for Semicalibrated Currents

created by spolaor on 24 Nov 2015
modified on 16 Oct 2018


Accepted Paper

Inserted: 24 nov 2015
Last Updated: 16 oct 2018

Journal: Adv. Math.
Year: 2018


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 $C^{3,\varepsilon_0}$ manifold, semicalibrated by a $C^{2,\varepsilon_0}$ $m$-form, has singular set of Hausdorff dimension at most $m-2$.

Keywords: Integral Currents, Semicalibrations, Regularity