  We present cosmological constraints derived from peak counts, minimum counts,
and the angular power spectrum of the Subaru Hyper Suprime-Cam first-year (HSC
Y1) weak lensing shear catalog. Weak lensing peak and minimum counts contain
non-Gaussian information and hence are complementary to the conventional
two-point statistics in constraining cosmology. In this work, we forward-model
the three summary statistics and their dependence on cosmology, using a suite
of $N$-body simulations tailored to the HSC Y1 data. We investigate systematic
and astrophysical effects including intrinsic alignments, baryon feedback,
multiplicative bias, and photometric redshift uncertainties. We mitigate the
impact of these systematics by applying cuts on angular scales, smoothing
scales, statistic bins, and tomographic redshift bins. By combining peaks,
minima, and the power spectrum, assuming a flat-$\Lambda$CDM model, we obtain
$S_{8} \equiv \sigma_8\sqrt{\Omega_m/0.3}= 0.810^{+0.022}_{-0.026}$, a 35\%
tighter constraint than that obtained from the angular power spectrum alone.
Our results are in agreement with other studies using HSC weak lensing shear
data, as well as with Planck 2018 cosmology and recent CMB lensing constraints
from the Atacama Cosmology Telescope and the South Pole Telescope.
