  We present a novel statistic to extract cosmological information in weak
lensing data: the lensing minima. We also investigate the effect of baryons on
the cosmological constraints from peak and minimum counts. Using the
\texttt{MassiveNuS} simulations, we find that lensing minima are sensitive to
non-Gaussian cosmological information and are complementary to the lensing
power spectrum and peak counts. For an LSST-like survey, we obtain $95\%$
credible intervals from a combination of lensing minima and peaks that are
significantly stronger than from the power spectrum alone, by $44\%$, $11\%$,
and $63\%$ for the neutrino mass sum $\sum m_\nu$, matter density $\Omega_m$,
and amplitude of fluctuation $A_s$, respectively. We explore the effect of
baryonic processes on lensing minima and peaks using the hydrodynamical
simulations \texttt{BAHAMAS} and \texttt{Osato15}. We find that ignoring
baryonic effects would lead to strong ($\approx 4 \sigma$) biases in inferences
from peak counts, but negligible ($\approx 0.5 \sigma$) for minimum counts,
suggesting lensing minima are a potentially more robust tool against baryonic
effects. Finally, we demonstrate that the biases can in principle be mitigated
without significantly degrading cosmological constraints when we model and
marginalize the baryonic effects.
