Soap films and covering spaces

DOI10.1007/BF02921771zbMath0848.49025MaRDI QIDQ1917959

Kenneth A. Brakke

Publication date: 28 October 1996

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

zbMATH Keywords

minimal surfacescurrentscalibrationcovering spacessoap filmsgeometric integration theoryflat chains

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items

Covers, soap films and BV functions, Volume-minimizing cycles in Grassmann manifolds, A first-order primal-dual algorithm for convex problems with applications to imaging, Calibrations for minimal networks in a covering space setting, Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone, Cartan's magic formula and soap film structures, Numerical Solution of Soap Film Dual Problems, An existence theorem for Brakke flow with fixed boundary conditions, Energy estimates for area minimizing hypersurfaces with arbitrary boundaries, A KIND OF SOAP FILM PROBLEM, Constrained BV functions on covering spaces for minimal networks and Plateau's type problems, An introduction to continuous optimization for imaging, On different notions of calibrations for minimal partitions and minimal networks in \(\mathbb{R}^2\), Plateau’s Problem

Uses Software

• Surface Evolver

Cites Work

• Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
• Calibrated geometries
• On the existence and regularity of fundamental domains with least boundary area
• Minimal cones on hypercubes
• Soap-film-like minimal surfaces spanning knots
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Soap films bounded by non-closed curves
• Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms
• Minimal surfaces, corners, and wires
• Minimal cones and the Bernstein problem
• Normal and integral currents
• Twisted Calibrations
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Solution of the Problem of Plateau
• Numerical Solution of Soap Film Dual Problems
• Boundary regularity and embedded solutions for the oriented Plateau problem
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