  The TeV-emitting BL Lac object Mkn 421 was observed with very long baseline
interferometry (VLBI) at three closely-spaced epochs one-month apart in
March-April 1998. The source was also monitored at very-high gamma-ray energies
(TeV measurements) during the same period in an attempt to search for
correlations between TeV variability and the evolution of the radio morphology
on parsec scales. While the VLBI maps show no temporal changes in the Mkn 421
VLBI jet, there is strong evidence of complex variability in both the total and
polarized fluxes of the VLBI core of Mkn 421 and in its spectrum over the
two-month span of our data. The high-energy measurements indicate that the
overall TeV activity of the source was rising during this period, with a
gamma-ray flare detected just three days prior to our second VLBI observing
run. Although no firm correlation can be established, our data suggest that the
two phenomena (TeV activity and VLBI core variability) are connected, with the
VLBI core at 22 GHz being the self-absorbed radio counterpart of synchrotron
self-Compton (SSC) emission at high energies. Based on the size of the VLBI
core, we could derive an upper limit of 0.1 pc (3 x 10**17 cm) for the
projected size of the SSC zone. This determination is the first model-free
estimate of the size of the gamma-ray emitting region in a blazar.
