  Minkowski functionals are summary statistics that capture the geometric and
morphological properties of fields. They are sensitive to all higher order
correlations of the fields and can be used to complement more conventional
statistics, such as the power spectrum of the field. We develop a Minkowski
functional-based approach for a full likelihood analysis of mildly non-Gaussian
sky maps with partial sky coverage. Applying this to the inference of
cosmological parameters from the Planck mission's map of the Cosmic Microwave
Background's lensing convergence, we find an excellent agreement with results
from the power spectrum-based lensing likelihood. While the non-Gaussianity of
current CMB lensing maps is dominated by reconstruction noise, a Minkowski
functional-based analysis may be able to extract cosmological information from
the non-Gaussianity of future lensing maps and thus go beyond what is
accessible with a power spectrum-based analysis. We make the numerical code for
the calculation of a map's Minkowski functionals, skewness and kurtosis
parameters available for download from GitHub.

Cosmology and Nongalactic Astrophysics