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]
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