  We discuss the results of a recent paper by Ekholm, Kova\v{r}\'ik and
Portmann in connection with a question of C. Guillarmou about the semiclassical
expansion of the lowest eigenvalue of the Pauli operator with Dirichlet
conditions. We exhibit connections with the properties of the torsion function
in mechanics, the exit time of a Brownian motion and the analysis of the low
eigenvalues of some Witten Laplacian.
