On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator

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.