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math.MG2026
The isoperimetric problem for four-dimensional parallelohedra
Matteo Novaga, Lark Song
The honeycomb and Kelvin problems ask how space can be partitioned into cells of equal volume with the least surface area. We resolve this question in four dimensions for convex bo…
math.MG2025
Periodic double tilings of the plane
Francesco Nobili, Matteo Novaga, Emanuele Paolini
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e.,…
math.MG2024
On the total surface area of potato packings
Matteo Novaga, Emanuele Paolini, Eugene Stepanov
We prove that if we fill without gaps a bag with infinitely many potatoes, in such a way that they touch each other in few points, then the total surface area of the potatoes must…