Discrete \(\ell^1\) double bubble solution is at most ceiling plus two of the continuous solution

DOI10.1007/s00454-023-00501-4OpenAlexW4366468203MaRDI QIDQ6151035

Parker Duncan, Eviatar B. Procaccia, Rory O'Dwyer

Publication date: 9 February 2024

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-023-00501-4

zbMATH Keywords

square latticeWulff shapediscrete isoperimetrydouble bubble problem

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Optimization of shapes other than minimal surfaces (49Q10) Isoperimetric problems for polytopes (52B60) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Related Items (2)

The double-bubble problem on the square lattice ⋮ A proof of finite crystallization via stratification

Cites Work

• Quenched invariance principle for simple random walk on clusters in correlated percolation models
• Concentration estimates for the isoperimetric constant of the supercritical percolation cluster
• The standard double soap bubble in \(\mathbb{R}^ 2\) uniquely minimizes perimeter
• The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
• Wulff clusters in \(\mathbb{R}^2\)
• The three dimensional polyominoes of minimal area
• Proof of the double bubble conjecture
• The Gaussian double-bubble and multi-bubble conjectures
• An elementary proof for the double bubble problem in \(\ell^1\) norm
• The Wulff crystal in Ising and percolation models. École d'Été de Probabilités de Saint-Flour XXXIV -- 2004
• Isoperimetry in Two-Dimensional Percolation
• Rigorous probabilistic analysis of equilibrium crystal shapes

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