The sizes of mini-voids in the local universe: an argument in favor of a
  warm dark matter model?
  Using high-resolution simulations within the Cold and Warm Dark Matter models
we study the evolution of small scale structure in the Local Volume, a sphere
of 8 Mpc radius around the Local Group. We compare the observed spectrum of
mini-voids in the Local Volume with the spectrum of mini-voids determined from
the simulations. We show that the \LWDM model can easily explain both the
observed spectrum of mini-voids and the presence of low-mass galaxies observed
in the Local Volume, provided that all haloes with circular velocities greater
than 20 km/s host galaxies. On the contrary within the LCDM model the
distribution of the simulated mini-voids reflects the observed one if haloes
with maximal circular velocities larger than 35 km/s host galaxies. This
assumption is in contradiction with observations of galaxies with circular
velocities as low as 20 km/s in our Local Universe. A potential problem of the
LWDM model could be the late formation of the haloes in which the gas can be
efficiently photo-evaporated. Thus star formation is suppressed and low-mass
haloes might not host any galaxy at all.
