Conference on Calculus of Variations in Lille - 3rd edition - July 4-6 2022

Isoperimetric problems on periodic lattices

Jul 6, 2022, 11:00 AM

1h

M2 building, Cité Scientifique - Meeting room, 1st floor (Laboratoire Paul Painlevé)

Speaker

Gian Paolo Leonardi (University of Trento )

Description

Motivated by the crystallization issue, we focus on the minimization of Heitman–Radin potential energies for configurations of $N$ particles in a periodic lattice, and in particular on the connection with anisotropic isoperimetric problems in the suitably rescaled limit as $N\to \mathrm{\infty }$. Besides identifying the asymptotic Wulff shapes through Gamma-convergence, we obtain fluctuation estimates for quasiminimizers that include the well-known $N^{3/4}$ conjecture for minimizers in planar lattices. Our technique combines the sharp quantitative Wulff inequality with a notion of quantitative closeness between discrete and continuum problems. These results have been obtained in collaborations with Marco Cicalese and Leonard Kreutz.