Journal of Convex Analysis 33 (2026), No. 1&2, 421--428
Copyright Heldermann Verlag 2026
A Note on the Honeycomb Optimality among Periodic Convex Tilings
Annalisa Cesaroni
Dip. di Matematica "Tullio Levi-Civita", Università di Padova, Padova, Italy
annalisa.cesaroni@unipd.it
Ilaria Fragalà
Dip. di Matematica, Politecnico di Milano, Milano, Italy
ilaria.fragala@polimi.it
Matteo Novaga
Dip. di Matematica, Università di Pisa, Pisa, Italy
matteo.novaga@unipi.it
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.
Keywords: Honeycomb conjecture, periodic convex tilings, Steiner symmetrization.
MSC: 52C20, 52C05, 51M20.
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