  Weak lensing surveys have become a powerful tool for mapping mass
distributions and constraining the expansion history of our Universe, but
continuum surveys must average over a large number of galaxies to average down
the ellipticity noise due to the unknown ellipticity and orientation of the
lensed galaxies. This Letter presents a technique for measuring weak lensing
with velocity maps that avoids the ellipticity noise. By studying the inherent
noise characteristics, we argue this new technique could rival or exceed the
sensitivity of traditional continuum observations for upcoming HI radio
surveys.
