Emanuele Paolini

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math.AP2026

Anisotropic isoperimetric double tilings of the plane

Francesco Nobili, Matteo Novaga, Emanuele Paolini

We study periodic partitions of the plane into two distinct cells minimizing the anisotropic $ℓ_{1}$ -perimeter. For a rectangular lattice $G$ , we compute explicitly the $(G,\ell_1…

math.AP2026

Optimal sets for a geometric oscillation energy

Matteo Novaga, Fumihiko Onoue, Emanuele Paolini

We investigate the nonlocal energy corresponding to the $p$ -oscillation of the unit normal vector for hypersurfaces, or the unit tangent vector for curves. The energy satisfies geo…

math.AP2025

Existence of a non-standard isoperimetric triple partition

Matteo Novaga, Emanuele Paolini, Vincenzo Maria Tortorelli

We show existence of a isoperimetric $3$ -partition of $R^{8}$ , with one set of finite volume and two of infinite volume, which is asymptotic to a singular minimal cone.