Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 32 min ago
PreprintarXiv licencearXiv

Tetrahedral points and classification of Almgren-minimizing sets in ℝ3

  • Michele Caselli
  • Zachary Lihn
Open at sourcePDFDOICite

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 ℝ3.

Related

  1. On a conjecture of Almgren: area-minimizing submanifolds with fractal singular sets
    Zhenhua Liu
    Annals of MathematicsPeer-reviewedLicence not statedFull text15 citedGeneral mathematicsOpenAlex
  2. Existence of flat blowups at boundary points of anisotropic minimizing hypercurrents
    Michael Novack, Reinaldo Resende
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  3. On Simon's area-minimizing hypersurfaces with fractal singular sets
    Zhenhua Liu
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Sofic systems and extreme points of self-affine limit sets
    Stefano Silvestri, Rodrigo A. Pérez
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  5. Large Planar Point Sets Contain 4 Collinear Points or Almost 7-Cliques, and Related Results
    Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +2
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{caselli2026tetrahedral,
  title = {{Tetrahedral points and classification of Almgren-minimizing sets in $\mathbbR^3$}},
  author = {Michele Caselli and Zachary Lihn},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24362},
  eprint = {2610.24362},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24362},
}
RIS
TY  - UNPB
TI  - Tetrahedral points and classification of Almgren-minimizing sets in ℝ^3
AU  - Michele Caselli
AU  - Zachary Lihn
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24362
UR  - https://arxiv.org/abs/2610.24362
AB  - 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 ℝ^3.
ER  -