Context :

Aims : We are presenting here a study of the cold dust in the close environs of the 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 against its environment .

Methods : We make use of 870 \mu m emission data obtained with the Large APEX Bolometer Camera ( LABOCA ) to map the dust emission .
The 870 \mu m emission provides an excellent probe of mass and density of dense molecular clouds .
The obtained LABOCA image was compared to archival infrared , radio continuum , and optical images .

Results : The 870 \mu m emission follows the 8 \mu m ( Spitzer ) , 250 \mu m , and 500 \mu m ( Herschel ) emission distributions showing the classical morphology of a two dimensional projection of a spherical shell .
We use the 870 \mu m and 250 \mu m 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 M _ { \odot } and 2800 M _ { \odot } , and volume densities between 1.1 \times 10 ^ { 3 } cm ^ { -3 } and \sim 2.04 \times 10 ^ { 5 } cm ^ { -3 } .
The total mass of the clumps is \sim 37600 M _ { \odot } .
The dust temperature of the clumps is in the range from 21 K to 32 K , while inside the H ii region reaches \sim 40 K. The clump mass distribution for the sample is well-fitted by a power law d N/ d log ( M /M _ { \odot } ) \propto M ^ { - \alpha } , with \alpha = 0.93 \pm 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 \mu m 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 their limits .
A comparison of the dynamical age of the H ii 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 .
The position of the identified young stellar objects in the region is also a strong indicator that the collect and collapse process is acting .

Conclusions :