We use recent observations of the HI-mass function to constrain galaxy formation. The data conflicts with the standard model where most of the gas in a low-mass dark matter halo is assumed to settle into a disk of cold gas that is depleted by star formation and supernova-driven outflows until the disk becomes gravitationally stable. A consistent model can be found if low-mass haloes are embedded in a preheated medium, with a specific gas entropy ~ 10Kev cm^2. Such a model simultaneously matches the faint-end slope of the galaxy luminosity function. We propose a preheating model where the medium around low-mass haloes is preheated by gravitational pancaking. Since gravitational tidal fields suppress the formation of low-mass haloes while promoting that of pancakes, the formation of massive pancakes precedes that of the low-mass haloes within them. We demonstrate that the progenitors of present-day dark matter haloes with M<10^{12}h^{-1}msun were embedded in pancakes of masses $~5x10^{12}h^{-1}msun$ at z~2. The formation of such pancakes heats the gas to a temperature of 5x10^5K and compresses it to an overdensity of ~10. Such gas has a cooling time that exceeds the age of the Universe at z~2, and has a specific entropy of ~15Kev cm^2, almost exactly the amount required to explain the stellar and HI mass functions. (Abridged)
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