Almgren's type regularity for semicalibrated currents

Luca Spolaor

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Submission date: 13. Jan. 2016
Pages: 59
published in: Advances in mathematics, 350 (2019), p. 747-815 
DOI number (of the published article): 10.1016/j.aim.2019.04.057
Bibtex
Keywords and phrases: geometric measure theory, Analysis and PDE, Regularity of Minimal Surfaces
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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,𝜀₀ manifold, semicalibrated by a C^2,𝜀₀ m-form, has singular set of Hausdorff dimension at most m − 2.