Speaker
Matteo Novaga
(University of Pisa)
Description
The classical Kelvin problem seeks the optimal equal-volume partition of $\mathbb R^d$ minimizing boundary surface area. In this talk, we present recent progress on periodic minimizing partitions in both isotropic and anisotropic settings.
Focusing first on two-dimensional configurations, we analyze optimal planar tilings and extend these techniques to higher dimensions, exploring connections with multi-bubble partitions, phase separation models, and periodic minimal surfaces, with emphasis on regularity, qualitative properties, and asymptotic volume regimes. Finally, we discuss the minimality of the regular truncated octahedron among all 3D parallelohedra.
The results are based on joint works with A. Cesaroni, F. Nobili and E. Paolini.
Author
Matteo Novaga
(University of Pisa)