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The presence of massive neutrinos affects structure formation, leavingimprints on large-scale structure observables such as the weak lensing field.The common lensing analyses with two-point statistics are insensitive to thelarge amount of non-Gaussian information in the density field. We investigatenon-Gaussian tools, in particular the Minkowski Functionals(MFs)---morphological descriptors including area, perimeter, and genus---in anattempt to recover the higher-order information. We use convergence maps fromthe Cosmological Massive Neutrino Simulations (\texttt{MassiveNus}) and assumegalaxy noise, density, and redshift distribution for an LSST-like survey. Weshow that MFs are sensitive to the neutrino mass sum, and the sensitivity isredshift dependent and is non-Gaussian. We find that redshift tomographysignificantly improves the constraints on neutrino mass for MFs, compared tothe improvements for the power spectrum. We attribute this to the strongerredshift dependence of neutrino effects on small scales. We then build anemulator to model the power spectrum and MFs, and study the constraints on$[M_{\nu}$, $\Omega_{m}$, $A_{s}]$ from the power spectrum, MFs, and theircombination. We show that MFs significantly outperform the power spectrum inconstraining neutrino mass, by more than a factor of four. However, a thoroughstudy of the impact from systematics such as baryon physics and galaxy shapeand redshift biases will be important to realize the full potential of MFs.

Constraining neutrino mass with weak lensing Minkowski Functionals