  Massive neutrinos suppress the growth of structure under their free-streaming
scales. The effect is most prominent on small scales where the widely-used
two-point statistics can no longer capture the full information. In this work,
we study the signatures massive neutrinos leave on large-scale structure (LSS)
as revealed by its morphological properties, which are fully described by $4$
Minkowski functionals (MFs), and quantify the constraints on the summed
neutrino mass $M_{\nu}$ from the MFs, by using publicly available N-body
simulations. We find the MFs provide important complementary information, and
give tighter constraints on $M_{\nu}$ than the power spectrum. Specifically,
depending on whether massive neutrinos are included in the density field (the
`m' field) or not (the `cb' field), we find the constraint on $M_{\nu}$ from
the MFs with a smoothing scale of $R_G=5 h^{-1}$Mpc is $48$ or $4$ times better
than that from the power spectrum. When the MFs are combined with the power
spectrum, they can improve the constraint on $M_{\nu}$ from the latter by a
factor of 63 for the `m' field and 5 for the `cb' field. Notably, when the `m'
field is used, the constraint on $M_{\nu}$ from the MFs can reach $0.0177$eV
with a volume of $1(h^{-1}\rm Gpc)^3$, while the combination of the MFs and
power spectrum can tighten this constraint to be $0.0133$eV, a $4.5\sigma$
significance on detecting the minimum sum of the neutrino masses. For the `m'
field, we also find the $\sigma_8$ and $M_{\nu}$ degeneracy is broken with the
MFs, leading to stronger constraints on all 6 cosmological parameters
considered in this work than the power spectrum.
