(abridged) Very long baseline interferometry (VLBI) observations at 86$,$GHz (wavelength, $lambda = 3,$mm) reach a resolution of about 50 $mu$as, probing the collimation and acceleration regions of relativistic outflows in active galactic nuclei. To extend the statistical studies of compact extragalactic jets, a large global 86 GHz VLBI survey of 162 radio sources was conducted in 2010-2011 using the Global Millimeter VLBI Array. The survey data attained a typical baseline sensitivity of 0.1 Jy and a typical image sensitivity of 5 mJy/beam, providing successful detections and images for all of the survey targets. For 138 objects, the survey provides the first ever VLBI images made at 86 GHz. Gaussian model fitting of the visibility data was applied to represent the structure of the sources. The Gaussian model-fit-based estimates of brightness temperature ($T_mathrm{b}$) at the jet base (core) and in moving regions (jet components) downstream from the core were compared to the estimates of $T_mathrm{b}$ limits made directly from the visibility data, demonstrating a good agreement between the two methods. The apparent brightness temperature estimates for the jet cores in our sample range from $2.5 times 10^{9},$K to $ 1.3times 10^{12},$K. A population model with a single intrinsic value of brightness temperature, $T_mathrm{0}$, is applied to reproduce the observed $T_mathrm{b}$ distribution. It yields $T_mathrm{0} = (3.77^{+0.10}_{-0.14}) times 10^{11},$K for the jet cores, implying that the inverse Compton losses dominate the emission. In the jet components, $T_mathrm{0} =(1.42^{+0.16}_{-0.19})times 10^{11},$K is found, slightly higher than the equipartition limit of $sim5times 10^{10},$K expected for these jet regions. For objects with sufficient structural detail detected, the adiabatic energy losses dominate the observed changes of $T_mathrm{b}$ along the jet.
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