Wulff clusters in \(\mathbb{R}^2\)

DOI10.1007/BF02922110zbMath0934.49024OpenAlexW2330970836MaRDI QIDQ1296923

Frank Morgan, Scott Greenleaf, Christopher P. French

Publication date: 4 April 2000

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

Full work available at URL: https://doi.org/10.1007/bf02922110

zbMATH Keywords

clustersWulff shapeenergy-minimizing

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Variational problems in a geometric measure-theoretic setting (49Q20) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (12)

Geometry of anisotropic double crystals ⋮ Clusters minimizing area plus length of singular curves ⋮ A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters ⋮ The double-bubble problem on the square lattice ⋮ Isoperimetric planar clusters with infinitely many regions ⋮ Discrete \(\ell^1\) double bubble solution is at most ceiling plus two of the continuous solution ⋮ On the Steiner property for planar minimizing clusters. The anisotropic case ⋮ Some regularity results for minimal crystals ⋮ Regularity results for boundaries in \(\mathbb R^2\) with prescribed anisotropic curvature ⋮ Existence of surface energy minimizing partitions of ℝⁿ satisfying volume constraints ⋮ An elementary proof for the double bubble problem in \(\ell^1\) norm ⋮ The Hexagonal Honeycomb Conjecture

Cites Work

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• Minimal surfaces, crystals, shortest networks, and undergraduate research
• Clusters minimizing area plus length of singular curves
• Existence of least-energy configurations of immiscible fluids
• The cone over the Clifford torus in \(R^ 4\) is \(\Phi\)-minimizing
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• Crystalline variational problems
• Lowersemicontinuity of energy clusters
• Flat Chains Over a Finite Coefficient Group

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