Clusters minimizing area plus length of singular curves

DOI10.1007/BF01459806zbMath0805.49025OpenAlexW2083038782MaRDI QIDQ1337529

Frank Morgan

Publication date: 9 November 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165230

zbMATH Keywords

clusterssoap bubblesurface area plus length

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75) Length, area, volume and convex sets (aspects of convex geometry) (52A38)

Related Items (21)

Some mathematical challenges in materials science ⋮ Isoperimetric inequalities in unbounded convex bodies ⋮ Regularity of isoperimetric regions that are close to a smooth manifold ⋮ Isoperimetric regions in the hyperbolic plane between parallel horocycles ⋮ A selection principle for the sharp quantitative isoperimetric inequality ⋮ On clusters and the multi-isoperimetric profile in Riemannian manifolds with bounded geometry ⋮ Lowersemicontinuity of energy clusters ⋮ Minimal hypersurfaces in \(\mathbb{R}^n\times\mathbf{S}^m\) ⋮ On the isoperimetric problem in Euclidean space with density ⋮ 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 ⋮ Surfaces Minimizing Area Plus Length of Singular Curves ⋮ Ground states of simple bodies that may undergo brittle fractures ⋮ Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension ⋮ Generalized compactness for finite perimeter sets and applications to the isoperimetric problem ⋮ Instability of the wet \(X\) soap film ⋮ Unnamed Item ⋮ Wulff clusters in \(\mathbb{R}^2\) ⋮ Existence of surface energy minimizing partitions of ℝⁿ satisfying volume constraints ⋮ Regularity results for some 1-homogeneous functionals

Cites Work

• Area minimizing hypersurfaces with prescribed volume and boundary
• The structure of stationary one dimensional varifolds with positive density
• Wulff clusters in \(\mathbb{R}^2\)
• Soap bubbles in \(\mathbb{R}^ 2\) and in surfaces
• The isoperimetric theorem for general integrands
• Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
• On the first variation of a varifold
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Mathematicians, Including Undergraduates, Look at Soap Bubbles
• Surfaces Minimizing Area Plus Length of Singular Curves
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