  The galaxy circular velocity function at small masses is related to the
matter power spectrum on small scales. Although this function is well-studied
for Local Group dwarfs, theoretical predictions and observational measurements
are difficult for satellite galaxies, because of ram pressure and tidal
stripping. By contrast, isolated dwarf galaxies are less affected by these
processes, and almost always have enough 21cm emission to trace their dynamics
robustly. Here, we test cold dark matter cosmology using isolated low mass
dwarf galaxies from the SDSS with measured 21cm widths. We find consistency
between the predicted and observed number density of isolated galaxies down to
circular velocities of 50 km/s. Our technique yields a direct test of
small-scale cosmology independent of the Lyman-alpha forest power spectrum, but
our sample is currently statistically less powerful: warm dark matter particles
heavier than 0.5 keV cannot be ruled out. Our major systematic uncertainty is
the surface brightness limit of the SDSS. Blind HI surveys, such as the ALFALFA
survey on Arecibo, will uncover a larger number of isolated low mass galaxies
and increase the power of our constraints. With our sample, we also find that
the Tully-Fisher relation for dwarf galaxies is a strong function of
environment, and that the baryonic fraction is only a weak function of mass.
These results suggest that for dwarf galaxies, gas loss is dominated by
external, not internal, processes. [abridged]
