We present Very Long Baseline Array (VLBA) images of 20 TeV blazars (HBLs) not previously well-studied on the parsec scale. Observations were made between August and December 2013, at a frequency of 8.4 GHz. These observations represent the first epoch of a VLBA monitoring campaign on these blazars, and they significantly increase the fraction of TeV HBLs studied with high-resolution imaging. The peak VLBI flux densities of these sources range from about 10 to 100 mJy/beam, and parsec-scale jet structure is detected in all sources. About half of the VLBI cores are resolved, with brightness temperature upper limits of a few times 10^10 K, and we find that a brightness temperature of about 2x10^10 K is consistent with the VLBI data for all but one of the sources. Such brightness temperatures do not require any relativistic beaming to reduce the observed value below commonly invoked intrinsic limits; however, the lack of detection of counter-jets does place a modest limit on the bulk Lorentz factor of greater than about 2. These data are thus consistent with a picture where weak-jet sources like the TeV HBLs develop significant velocity structures on parsec-scales. We also extend consideration to the full sample of TeV HBLs by combining the new VLBI data with VLBI and gamma-ray data from the literature. By comparing measured VLBI and TeV fluxes to samples with intrinsically uncorrelated luminosities generated by Monte Carlo simulations, we find a marginally significant correlation between the VLBI and TeV fluxes for the full TeV HBL sample.
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