Work

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

Year: 2026

Type: preprint

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 $\mathbb{R}^3$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.24362

Authors: Caselli, Michele, Lihn, Zachary

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223019874

Cites: 18

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Related to: 10