  We present simultaneous, sub-arcsecond (<=50pc) resolution 5 GHz, 8.4 GHz,
and 15 GHz VLA observations of a well-defined sample of sixteen low-luminosity
active galactic nuclei (LLAGNs). The radio emission in most of these nuclei
does not show the rising spectrum (0.2 <= s <= 1.3, L_nu propto nu^{s})
expected from thermal electrons in an advection dominated accretion flow (ADAF)
with or without weak to moderately-strong outflows. Rather, the flat radio
spectra are indicative of either synchrotron self-absorbed emission from jets,
convection-dominated accretion flows (CDAFs) with L >= 10^{-5} L_Edd, or ADAFs
with strong (p >= 0.6) outflows. The jet interpretation is favored by three
factors: a) the detection of pc-scale radio extensions, morphologically
reminiscent of jets, in the five nuclei with the highest peak radio
flux-density; b) the domination of parsec-scale jet radio emission over
unresolved `core' emission in the three best-studied nuclei; and c) the lack of
any clear correlation between radio spectral shape and black hole mass as would
be expected from the dependence of the radio turnover frequency on black hole
mass in ADAF and CDAF models. A jet domination of nuclear radio emission
implies significantly lower accretion rates in ADAF-type models than earlier
estimated from core radio luminosities.
