On the honeycomb conjecture for Robin Laplacian eigenvalues

DOI10.1142/S0219199718500074zbMath1414.49044arXiv1706.10055WikidataQ122988398 ScholiaQ122988398MaRDI QIDQ4630364

Dorin Bucur, Ilaria Fragalà

Publication date: 26 March 2019

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.10055

zbMATH Keywords

optimal partitionshoneycombRobin Laplacian eigenvalues\(\alpha\)-Cheeger constant

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Variational methods for second-order elliptic equations (35J20) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Inequalities and extremum problems in real or complex geometry (51M16) Variational methods for eigenvalues of operators (49R05)

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Proof of the honeycomb asymptotics for optimal Cheeger clusters ⋮ Mean-to-max ratio of the torsion function and honeycomb structures ⋮ Asymptotic optimality of the triangular lattice for a class of optimal location problems ⋮ Phase field approach to optimal packing problems and related Cheeger clusters

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