Abstract

We show that the hexagonal honeycomb is optimal among convex periodic tessellations of the plane, provided the cost functional is lower semicontinuous with respect to the Hausdorff convergence, and decreasing under Steiner symmetrization.

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Keywords

  • Honeycomb conjecture
  • periodic convex tilings
  • Steiner symmetrization

Mathematics Subject Classification

52C20, 52C05, 51M20

Suggested citation

A. Cesaroni, I. Fragalà, M. Novaga. “A Note on the Honeycomb Optimality among Periodic Convex Tilings.” Journal of Convex Analysis 33 (2026), No. 1&2, 421–428.

Copyright Heldermann Verlag 2026