On the honeycomb conjecture for Robin Laplacian eigenvalues

Dorin Bucur; Ilaria Fragala

arxiv: 1706.10055 · v1 · pith:W3DL5HQNnew · submitted 2017-06-30 · 🧮 math.OC · math.AP· math.SP

On the honeycomb conjecture for Robin Laplacian eigenvalues

Dorin Bucur , Ilaria Fragala This is my paper

classification 🧮 math.OC math.APmath.SP

keywords robinhoneycomblaplacianasymptoticallycellscheegerclusterconjecture

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We prove that the optimal cluster problem for the sum of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity.

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On the honeycomb conjecture for Robin Laplacian eigenvalues

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