We report Hubble Space Telescope Cosmic Origins Spectrograph far-ultraviolet and Arecibo Telescope H 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 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 i masses \approx ( 0.24 - 5.2 ) \times 10 ^ { 9 } \ > { M } _ { \odot } , lower than the knee of the local H 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 i 21 cm or CO emission line widths , \Delta V _ { 20 } \approx 100 - 290 km s ^ { -1 } , and high gas fractions , f _ { HI } \approx 5 - 100 , suggesting that the absorber hosts are gas-rich galaxies with low star formation efficiencies . However , the H i 21 cm velocity spreads ( \gtrsim 100 km s ^ { -1 } ) appear systematically larger than the velocity spreads in typical dwarf galaxies .