Local 𝐶^{1,𝛽}-regularity at the boundary of two dimensional sliding almost minimal sets in ℝ³

DOI10.1090/btran/40zbMath1459.49015arXiv1611.01343OpenAlexW3170767940MaRDI QIDQ5853607

Yangqin Fang

Publication date: 11 March 2021

Published in: Transactions of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.01343

zbMATH Keywords

regularityHausdorff measurePlateau's problemblow-up limitalmost minimal setssliding boundary conditionsnormalized Hausdorff distance

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Optimality conditions (49K99) Existence theories in calculus of variations and optimal control (49J99)

Related Items (2)

A local description of 2-dimensional almost minimal sets bounded by a curve ⋮ On the equality between the infima obtained by solving various Plateau's problems

Cites Work

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• \(C^{1+\alpha}\)-regularity for two-dimensional almost-minimal sets in \(\mathbb R^n\)
• A generalization of Reifenberg's theorem in \({\mathbb{R}}^3\)
• Hölder regularity of two-dimensional almost-minimal sets in \(\mathbb R^n\)
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Hölder regularity at the boundary of two-dimensional sliding almost minimal sets
• On the first variation of a varifold
• Should we solve Plateau's problem again?
• Local Regularity Properties of Almost and Quasiminimal sets with a Sliding Boundary Condition

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