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math.MG2026
The rhombic dodecahedral conjecture
Annalisa Cesaroni, Matteo Novaga
We prove that every three-dimensional parallelohedron satisfies \[ \mathcal H^2(\partial P)\ge 12\sqrt2\,r(P)^2, \] where is the inradius of , with equality if and on…
math.MG2026
The truncated octahedron minimizes surface area among parallelohedra of equal volume
Annalisa Cesaroni, Matteo Novaga
We prove that the regular truncated octahedron uniquely minimizes surface area among all parallelohedra of fixed volume. Equivalently, every three-dimensional parallelohedron s…
math.MG2026
Local minimality of the truncated octahedron for the isoperimetric problem on parallelohedra
Annalisa Cesaroni, Matteo Novaga
We investigate the isoperimetric problem for the Voronoi cells of three-dimensional lattices. Using Selling parameters, we derive an explicit closed formula for the scale-invariant…