Cosmological Applications of the Gaussian Kinematic Formula
  The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an
extremely powerful tool allowing for explicit analytic predictions of expected
values of Minkowski functionals under realistic experimental conditions for
cosmological data collections. In this paper, we implement Minkowski
functionals on multipoles and needlet components of CMB fields, thus allowing a
better control of cosmic variance and extraction of information on both
harmonic and real domains; we then exploit the GKF to provide their expected
values on spherical maps, in the presence of arbitrary sky masks, and under
nonGaussian circumstances. All our results are validated by numerical
experiments, which show a perfect agreement between theoretical predictions and
Monte Carlo simulations.
