I will present a joint work with Agnès Desolneux (CNRS, Centre Borelli, ENS Paris-Saclay) on the geometry of excursion sets of smooth stationary Gaussian fields.

In this work we focus on the effect of anisotropy on their Lipschitz-Killing curvature densities (close from area, perimeter and Euler characteristics of excursion sets) and propose a new geometrical index of anisotropy, closely linked with isoperimetric inequalities.