Weak approach to planar soap bubble clusters

zbMath1257.53017MaRDI QIDQ1925597

Wacharin Wichiramala

Publication date: 18 December 2012

Published in: Missouri Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.mjms/1352138562

zbMATH Keywords

least perimetersoap bubbleminimizing enclosure

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Optimization of shapes other than minimal surfaces (49Q10)

Cites Work

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• Existence and uniqueness of standard bubble clusters of given volumes in \(\mathbb R^n\)
• The standard double soap bubble in \(\mathbb{R}^ 2\) uniquely minimizes perimeter
• The double bubble problem on the cone
• Double bubbles in \(\mathbb S^3\) and \(\mathbb H^3\)
• Proof of the double bubble conjecture in \(\mathbb R^n\)
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Soap bubbles in \(\mathbb{R}^ 2\) and in surfaces
• Proof of the double bubble conjecture
• The double bubble problem in spherical and hyperbolic space
• Proof of the double bubble conjecture in \(\mathbb{R}^4\) and certain higher dimensional cases.
• The shortest enclosure of three connected areas in \(\mathbb{R}^ 2\)
• The perimeter-minimizing enclosure of two areas in \(S^2\)
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• The standard double bubble is the unique stable double bubble in $\mathbf {R}^2$
• Proof of the planar triple bubble conjecture
• Double Bubbles in the Three-Torus
• The double bubble problem on the flat two-torus
• Least-perimeter partitions of the disk into three regions of given areas
• The shortest enclosure of two connected regions in a corner

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