The standard double bubble is the unique stable double bubble in $\mathbf {R}^2$

DOI10.1090/S0002-9939-02-06640-6zbMath1003.53010MaRDI QIDQ4330601

Wacharin Wichiramala, Frank Morgan

Publication date: 13 May 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

soap bubblestable double bubblestandard double bubble

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20)

Related Items

Double Bubbles in the Three-Torus, The double bubble problem on the flat two-torus, Minimal cluster computation for four planar regions with the same area, Double bubbles with high constant mean curvatures in Riemannian manifolds, Weak approach to planar soap bubble clusters, Uniform bound on the number of partitions for optimal configurations of the Ohta–Kawasaki energy in 3D, Minimal clusters of four planar regions with the same area, The quadruple planar bubble enclosing equal areas is symmetric, Proof of the planar triple bubble conjecture, The length of the shortest closed geodesic on positively curved 2-spheres

Cites Work

• The standard double soap bubble in \(\mathbb{R}^ 2\) uniquely minimizes perimeter
• The structure of singularities in solutions to ellipsoidal variational problems with constraints in \(R^3\)
• Soap bubbles in \(\mathbb{R}^ 2\) and in surfaces
• The double bubble problem in spherical and hyperbolic space
• Proof of the double bubble conjecture in \(\mathbb{R}^4\) and certain higher dimensional cases.
• OPEN PROBLEMS IN SOAP BUBBLE GEOMETRY
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• ( M , ɛ, δ)-Minimal Curve Regularity
• Proof of the planar triple bubble conjecture
• Proof of the double bubble conjecture
• Unnamed Item