On the minimality of x/|x|

par Xavier Lamy (IMT)

jeudi 15 oct. 2026, 11:15 → 12:15 Europe/Paris

Salle J. Cavailles (1R2-132)

The map $u_*\colon\mathbb R^{^3}\to\mathbb S^{^2}$, $x\mapsto x/|x|$, is a local minimizer of the Dirichlet energy $\int |\nabla u|^2$ among $\mathbb S^{^2}$-valued maps. I will present recent results, and open questions, about quantitative versions of that statement and its extension to a family of energies arising from the physics of liquid crystals. This is joint work with Pierre Bousquet.