Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents

2024/09/04 by Minter, Paul, Parise, Davide, Skorobogatova, Anna +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.03037

Abstract

We prove that the singular set of an m-dimensional integral current T in ℝ^{n + m}, semicalibrated by a C^{2, κ₀} m-form ω is countably (m - 2)-rectifiable. Furthermore, we show that there is a unique tangent cone at H^{m - 2}-a.e. point in the interior singular set of T. Our proof adapts techniques that were recently developed in [DLS23a, DLS23b, DLMS23] for area-minimizing currents to this setting.

Cited by

• Hausdorff measure bounds for density-Q flat singularities of minimizing integral currents

Related

• The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and H^m-2-a.e. Uniqueness of Tangent Cones
• Uniqueness of tangent cones for 2-dimensional almost minimizing currents
• The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points
• The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than 1
• Fine Structure of Singularities in Area-Minimizing Currents Mod(q)