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Minkowski functionals are summary statistics that capture the geometric andmorphological properties of fields. They are sensitive to all higher ordercorrelations of the fields and can be used to complement more conventionalstatistics, such as the power spectrum of the field. We develop a Minkowskifunctional-based approach for a full likelihood analysis of mildly non-Gaussiansky maps with partial sky coverage. Applying this to the inference ofcosmological parameters from the Planck mission's map of the Cosmic MicrowaveBackground's lensing convergence, we find an excellent agreement with resultsfrom the power spectrum-based lensing likelihood. While the non-Gaussianity ofcurrent CMB lensing maps is dominated by reconstruction noise, a Minkowskifunctional-based analysis may be able to extract cosmological information fromthe non-Gaussianity of future lensing maps and thus go beyond what isaccessible with a power spectrum-based analysis. We make the numerical code forthe calculation of a map's Minkowski functionals, skewness and kurtosisparameters available for download from GitHub.

A Minkowski Functional Analysis of the Cosmic Microwave Background Weak Lensing Convergence