On the honeycomb conjecture for a class of minimal convex partitions

DOI10.1090/tran/7326zbMath1396.52024arXiv1703.05383OpenAlexW2600489988WikidataQ123122735 ScholiaQ123122735MaRDI QIDQ4580354

Gianmaria Verzini, Bozhidar Velichkov, Dorin Bucur, Ilaria Fragalà

Publication date: 15 August 2018

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

Full work available at URL: https://arxiv.org/abs/1703.05383

zbMATH Keywords

Cheeger constantlogarithmic capacityoptimal partitionshoneycomb conjecturediscrete Faber-Krahn inequality

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Inequalities and extremum problems in real or complex geometry (51M16)

Related Items

Proof of the honeycomb asymptotics for optimal Cheeger clusters ⋮ Mean-to-max ratio of the torsion function and honeycomb structures ⋮ The Cheeger problem in abstract measure spaces ⋮ On the honeycomb conjecture for Robin Laplacian eigenvalues ⋮ Asymptotic optimality of the triangular lattice for a class of optimal location problems ⋮ Optimal partitions for Robin Laplacian eigenvalues ⋮ Optimal partitioning of an interval and applications to Sturm-Liouville eigenvalues ⋮ Phase field approach to optimal packing problems and related Cheeger clusters ⋮ The Cheeger N-problem in terms of BV functions ⋮ Dimensional lower bounds for contact surfaces of Cheeger sets ⋮ Large \(m\) asymptotics for minimal partitions of the Dirichlet eigenvalue

Cites Work

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• A Faber-Krahn inequality for the Cheeger constant of \(N\)-gons
• Extremality conditions and regularity of solutions to optimal partition problems involving Laplacian eigenvalues
• Cheeger \(N\)-clusters
• On spectral minimal partitions: a survey
• Nodal domains and spectral minimal partitions
• The honeycomb conjecture
• Computing ultra-precise eigenvalues of the Laplacian within polygons
• On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae
• The Brunn-Minkowski inequality for the \(n\)-dimensional logarithmic capacity of convex bodies
• An optimal partition problem related to nonlinear eigenvalues.
• An isoperimetric inequality for logarithmic capacity of polygons
• Characterization of Cheeger sets for convex subsets of the plane
• An optimal partition problem for eigenvalues
• A note on the stability of the Cheeger constant of $N$-gons
• An Overview on the Cheeger Problem
• The Hexagonal Honeycomb Conjecture
• Hexagonal Economic Regions Solve the Location Problem
• Numerical simulations for nodal domains and spectral minimal partitions
• A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results