Geometrical estimators as a test of Gaussianity in the cosmic microwave background

We investigate the power of geometrical estimators on detecting non-Gaussia nity in the cosmic microwave background (CMB). In particular the number, ec centricity and Gaussian curvature of excursion sets above (and below) a thr eshold are studied. We compare their different performance when applied to non-Gaussian simulated maps of small patches of the sky, which take into ac count the angular resolution and instrumental noise of the Planck satellite . These non-Gaussian simulations are obtained as perturbations of a Gaussia n field in two different ways which introduce a small level of skewness or kurtosis in the distribution. A comparison with a classical estimator, the genus, is also shown. We find that the Gaussian curvature is the best of ou r estimators in all the considered cases. Therefore we propose the use of t his quantity as a particularly useful test to look for non-Gaussianity in t he CMB.