  Current explanation of the overabundance of dark matter subhalos in the Local
Group (LG) indicates that there maybe a limit on mass of a halo, which can host
a galaxy. This idea can be tested using voids in the distribution of galaxies:
at some level small voids should not contain any (even dwarf) galaxies. We use
observational samples complete to M_B=-12 with distances less than 8 Mpc to
construct the void function (VF): the distribution of sizes of voids empty of
any galaxies. There are ~ 30 voids with sizes ranging from 1 to 5 Mpc. We also
study the distribution of dark matter halos in very high resolution simulations
of the LCDM model. The theoretical VF matches the observations remarkably well
only if we use halos with circular velocities larger than 45 +/- 10 km/s. This
agrees with the Local Group predictions. Small voids look quite similar to heir
giant cousins: the density has a minimum at the center of a void and it
increases as we get closer to the border. Thus, both the Local Group data and
the nearby voids indicate that isolated halos below 45 +/- 10 km/s must not
host galaxies and that small (few Mpc) voids are truly dark.
