We report Hubble Space Telescope Cosmic Origins Spectrograph far-ultraviolet and Arecibo Telescope H{sc i} 21cm spectroscopic studies of six damped and sub-damped Lyman-$alpha$ absorbers (DLAs and sub-DLAs, respectively) at $z lesssim 0.1$, that have yielded estimates of their H{sc i} column density, metallicity and atomic gas mass. This significantly increases the number of DLAs with gas mass estimates, allowing the first comparison between the gas masses of DLAs and local galaxies. Including three absorbers from the literature, we obtain H{sc i} masses $approx (0.24 - 5.2) times 10^9 : {rm M}_odot$, lower than the knee of the local H{sc i} mass function. This implies that massive galaxies do not dominate the absorption cross-section for low-$z$ DLAs. We use Sloan Digital Sky Survey photometry and spectroscopy to identify the likely hosts of four absorbers, obtaining low stellar masses, $approx 10^7-10^{8.7} M_odot$, in all cases, consistent with the hosts being dwarf galaxies. We obtain high H{sc i} 21,cm or CO emission line widths, $Delta V_{20} approx 100-290$~km~s$^{-1}$, and high gas fractions, $f_{rm HI} approx 5-100$, suggesting that the absorber hosts are gas-rich galaxies with low star formation efficiencies. However, the H{sc i} 21,cm velocity spreads ($gtrsim 100$~km~s$^{-1}$) appear systematically larger than the velocity spreads in typical dwarf galaxies.
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