  The mean and the scatter of the HI content of a dark-matter halo as a
function of the halo mass are useful statistics that can be used to test models
of structure and galaxy formation. We investigate the possibility of
constraining this HI-halo mass relation (HIHMR) from intensity maps of the
redshifted 21 cm line. In particular, we use the geometry and topology of the
brightness-temperature isocontours in a single frequency channel as quantified
by the Minkowski functionals. First, we generate mock maps from a large N-body
simulation considering the impact of thermal noise and foreground removal. We
then use the Fisher information formalism to forecast constraints on a
parametric model for the HIHMR. We consider a 20,000 deg$^2$ survey (originally
proposed for dark-energy science) conducted with the Square Kilometre Array
Phase 1 (SKA-1) MID observatory operating in single-dish mode. For a channel
bandwidth of 2 MHz, we show that an integration time of a few$\,\times\,10^4$ s
per pointing is sufficient to image the smoothed HI distribution at redshift $z
\simeq 1$ and to measure the HIHMR in a nearly optimal way from the Minkowski
functionals. Tighter constraints on some of the parameters can be obtained by
using also an independent measurement of the mean HI density. Combining the
results from different frequency channels provides exquisite constraints on the
evolution of the HIHMR, especially in the central frequency range of the data
cube.
