Year: 2026
Type: preprint
Abstract: We characterize the minimizers of the anisotropic perimeter in the flat torus under an area constraint. We show that, depending on the area, the periodic global minimizer undergoes two phase transitions, changing from a droplet (a rescaled Wulff shape) to a flat band wrapping around the torus in a preferred direction determined by the anisotropy (lamellar phase), and finally to a bubble (the complement of a rescaled Wulff shape). For certain non-symmetric surface tensions, the lamellar phase is absent altogether; for other non regular surface tensions, there exist infinitely many minimizing configurations coexisting with the lamellar phase.
Source: arXiv (Cornell University)
Authors: Bonacini, Marco, Fiorini, Alberto
Institution: University of Trento
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212062056
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