cvgmt: Tetrahedral points and classification of Almgren-minimizing sets in $\mathbb{R}^3$

Calculus of Variations and Geometric Measure Theory

M. Caselli - Z. Lihn

Tetrahedral points and classification of Almgren-minimizing sets in $\mathbb{R}^3$

created by caselli on 16 Oct 2026

[BibTeX]

Preprint

Inserted: 16 oct 2026
Last Updated: 16 oct 2026

Year: 2026

Abstract:

We prove that a two-dimensional Almgren-minimizing set in three dimensions which is sufficiently close in Hausdorff distance to a tetrahedral cone contains an interior tetrahedral point. As a consequence, we obtain quantitative regularity near tetrahedral cones and we complete the classification of entire Almgren-minimizers in $\mathbb{R}^3$.

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Almgren_T_Points.pdf