Soap film solutions to Plateau's problem

DOI10.1007/s12220-012-9337-xzbMath1302.49059arXiv1106.5839OpenAlexW2057742613WikidataQ56227808 ScholiaQ56227808MaRDI QIDQ472002

Jenny Harrison

Publication date: 18 November 2014

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5839

zbMATH Keywords

differential formscompactnessPlateau's problemPoincaré lemmaarea-minimizing surfacesdifferential chains

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items

Solution of the Kirchhoff-Plateau problem ⋮ Existence and soap film regularity of solutions to Plateau's problem ⋮ Existence of solutions to a general geometric elliptic variational problem ⋮ Towards geometric integration of rough differential forms ⋮ General methods of elliptic minimization ⋮ The regularity theory for the area functional (in geometric measure theory) ⋮ A direct approach to Plateau's problem in any codimension ⋮ Simulation of a Soap Film Möbius Strip Transformation ⋮ Soap film spanning an elastic link ⋮ An existence theorem for Brakke flow with fixed boundary conditions ⋮ Solutions to the Reifenberg plateau problem with cohomological spanning conditions ⋮ Roughening it — evolving irregular domains and transport theorems ⋮ Constrained BV functions on covering spaces for minimal networks and Plateau's type problems ⋮ A direct approach to Plateau's problem ⋮ Plateau’s Problem ⋮ Plateau's Problem as a Singular Limit of Capillarity Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
• On the oriented Plateau problem
• Cartan's magic formula and soap film structures
• On Plateau's problem for soap films with a bound on energy
• Operator calculus of differential chains and differential forms
• Normal and integral currents
• A proof of the regularity everywhere of the classical solution to Plateau's problem
• Regularity of minimizing surfaces of prescribed mean curvature
• Verzweigungspunkte von H-Flächen. II
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Flat Chains Over a Finite Coefficient Group
• Integral Currents Mod 2
• Boundary regularity and embedded solutions for the oriented Plateau problem

This page was built for publication: Soap film solutions to Plateau's problem