Minimal clusters of four planar regions with the same area

DOI10.1051/cocv/2017066zbMath1411.53013arXiv1612.00178OpenAlexW3106109160MaRDI QIDQ4646833

A. Tamagnini, Emmanuele Paolini

Publication date: 21 December 2018

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.00178

zbMATH Keywords

separationplanar networksminimal clusters

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Discrete geometry (52C99)

Related Items (7)

Minimal cluster computation for four planar regions with the same area ⋮ On the Steiner property for planar minimizing clusters. The isotropic case ⋮ A formula for the minimal perimeter of clusters with density ⋮ On the Steiner property for planar minimizing clusters. The anisotropic case ⋮ The quadruple planar bubble enclosing equal areas is symmetric ⋮ Sticky-disk limit of planar \(N\)-bubbles ⋮ Perimeter-minimizing triple bubbles in the plane and the 2-sphere

Uses Software

• Sandwich

Cites Work

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• The honeycomb conjecture
• Proof of the double bubble conjecture
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• OPEN PROBLEMS IN SOAP BUBBLE GEOMETRY
• Sets of Finite Perimeter and Geometric Variational Problems
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• The Hexagonal Honeycomb Conjecture
• The standard double bubble is the unique stable double bubble in $\mathbf {R}^2$
• Proof of the planar triple bubble conjecture

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