Global regularity for minimal sets near a \(\mathbb{T}\)-set and counterexamples

DOI10.4171/RMI/775zbMath1290.49092arXiv1112.3565OpenAlexW2963110431WikidataQ124837944 ScholiaQ124837944MaRDI QIDQ2449578

Xiangyu Liang

Publication date: 8 May 2014

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3565

zbMATH Keywords

knotsHausdorff measureminimal setsblow-in limitexistence of singularities

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75)

Related Items (2)

Global regularity for minimal sets near a union of two planes ⋮ Limits of topological minimal sets with finitely generated coefficient groups

Cites Work

• Topological minimal sets and existence results
• \(C^{1+\alpha}\)-regularity for two-dimensional almost-minimal sets in \(\mathbb R^n\)
• Hölder regularity of two-dimensional almost-minimal sets in \(\mathbb R^n\)
• Singular sets of minimizers for the Mumford-Shah functional
• Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms
• Differential Topology
• Almgren-minimality of unions of two almost orthogonal planes in ℝ⁴
• Uniform rectifiability and quasiminimizing sets of arbitrary codimension

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