Topological minimal sets and existence results

DOI10.1007/s00526-012-0526-zzbMath1271.49033OpenAlexW2139525740MaRDI QIDQ353108

Xiangyu Liang

Publication date: 12 July 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-012-0526-z

zbMATH Keywords

existence resultsMumford-Shah-minimal setstopological minimal sets

Mathematics Subject Classification ID

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

Related Items

Sliding stability and uniqueness for the set \((Y \times Y\), On the Almgren minimality of the product of a paired calibrated set and a calibrated manifold of codimension 1, On the Almgren minimality of the product of a paired calibrated set with a calibrated set of codimension 1 with singularities, and new Almgren minimal cones, Global regularity for minimal sets near a \(\mathbb{T}\)-set and counterexamples, Uniqueness property for \(2\)-dimensional minimal cones in \(\mathbb{R}^3\), A direct approach to Plateau's problem, Almgren and topological minimality for the set \(Y\times Y\), Limits of topological minimal sets with finitely generated coefficient groups

Cites Work

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• Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
• 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
• Size minimization and approximating problems
• Singular sets of minimizers for the Mumford-Shah functional
• Some wild cells and spheres in three-dimensional space
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Differential Topology
• Uniform rectifiability and quasiminimizing sets of arbitrary codimension