Surfaces Minimizing Area Plus Length of Singular Curves

DOI10.2307/2161184zbMath0816.49033OpenAlexW4238591035MaRDI QIDQ4318347

Frank Morgan

Publication date: 13 July 1995

Full work available at URL: https://doi.org/10.2307/2161184

zbMATH Keywords

singular curvesphysical examplesenergy-minimizing interfacessurfaces minimizing area plus length

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20)

Related Items

The Surface Evolver ⋮ Clusters minimizing area plus length of singular curves ⋮ Crystals and polycrystals in \(\mathbb R^n\): lower semicontinuity and existence ⋮ The \(c\)-isoperimetric mass of currents and the \(c\)-Plateau problem ⋮ Stability of spherical caps under the volume-preserving mean curvature flow with line tension ⋮ Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension ⋮ On the thread problem for minimal surfaces

Uses Software

• Surface Evolver

Cites Work

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• Curves length-minimizing modulo \(\nu\) in \(R^ n\)
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• Minimal cones on hypercubes
• On the first variation of a varifold: Boundary behavior
• The structure of singularities in solutions to ellipsoidal variational problems with constraints in \(R^3\)
• Clusters minimizing area plus length of singular curves
• Die Existenz einer Minimalfläche mit freiem Rand vorgeschriebener Länge
• Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms
• Ein einfacher Beweis für die Regularität der Lösungen gewisser zweidimensionaler Variationsprobleme unter freien Randbedingungen
• Optimal approximations by piecewise smooth functions and associated variational problems
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• The Surface Evolver
• Problems Connected with Convexity
• On boundary regularity for Plateau's problem
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension

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