Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

The rhombic dodecahedral conjecture

created by novaga on 19 Sep 2026

[BibTeX]

Preprint

Inserted: 19 sep 2026
Last Updated: 19 sep 2026

Year: 2026

Abstract:

We prove that every three-dimensional parallelohedron $P$ satisfies \[ \mathcal H^2(\partial P)\ge 12\sqrt2\,r(P)^2, \] where $r(P)$ is the inradius of $P$, with equality if and only if $P$ is similar to the regular rhombic dodecahedron.


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