  We are presenting here a study of the cold dust in the infrared ring nebula
Gum 31. We aim at deriving the physical properties of the molecular gas and
dust associated with the nebula, and investigating its correlation with the
star formation in the region, that was probably triggered by the expansion of
the ionization front. We use 870 micron data obtained with LABOCA to map the
dust emission. The obtained LABOCA image was compared to archival IR,radio
continuum, and optical images. The 870 micron emission follows the 8 micron
(Spitzer), 250 micron, and 500 micron (Herschel) emission distributions showing
the classical morphology of a spherical shell. We use the 870 micron and 250
micron images to identify 60 dust clumps in the collected layers of molecular
gas using the Gaussclumps algorithm. The clumps have effective deconvolved
radii between 0.16 pc and 1.35 pc, masses between 70 Mo and 2800 Mo, and volume
densities between 1.1x10^3 cm^-3 and 2.04x10^5 cm^-3. The total mass of the
clumps is 37600 Mo. The dust temperature of the clumps is in the range from 21
K to 32 K, while inside the HII region reaches ~ 40 K. The clump mass
distribution is well-fitted by a power law dN/dlog(M/Mo) proportional to
M^(-alpha), with alpha=0.93+/-0.28. The slope differs from those obtained for
the stellar IMF in the solar neighborhood, suggesting that the clumps are not
direct progenitors of single stars/protostars. The mass-radius relationship for
the 41 clumps detected in the 870 microns emission shows that only 37% of them
lie in or above the high-mass star formation threshold, most of them having
candidate YSOs projected inside. A comparison of the dynamical age of the HII
region with the fragmentation time, allowed us to conclude that the collect and
collapse mechanism may be important for the star formation at the edge of Gum
31, although other processes may also be acting.
