Global regularity for minimal sets near a union of two planes

DOI10.5802/aif.3058zbMath1366.49058arXiv1203.0560OpenAlexW2515409637MaRDI QIDQ507097

Xiangyu Liang

Publication date: 3 February 2017

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0560

zbMATH Keywords

Hausdorff measureelliptic systemsminimal 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) Optimization of shapes other than minimal surfaces (49Q10) Optimality conditions (49K99)

Cites Work

• Unnamed Item
• Unnamed Item
• \(C^{1+\alpha}\)-regularity for two-dimensional almost-minimal sets in \(\mathbb R^n\)
• Hölder regularity of two-dimensional almost-minimal sets in \(\mathbb R^n\)
• Size-minimizing rectifiable currents
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Singular sets of minimizers for the Mumford-Shah functional
• Geometric measure theory.
• Global regularity for minimal sets near a \(\mathbb{T}\)-set and counterexamples
• Almgren and topological minimality for the set \(Y\times Y\)
• On the first variation of a varifold
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Harnack-type mass bounds and bernstein theorems for area-minimizing flat chains modulo v.
• Almgren-minimality of unions of two almost orthogonal planes in ℝ⁴
• Uniform rectifiability and quasiminimizing sets of arbitrary codimension