  Observations of gamma-ray bursts (GRBs) at Very High Energy (VHE) offer a
unique opportunity to investigate particle acceleration processes, magnetic
fields and radiation fields in these events. Very Long Baseline Interferometry
(VLBI) observations have been proven to be a powerful tool providing unique
information on the source size of the GRBs at mas scales, as well as their
accurate positions and possible expansion speeds. This paper reports on the
follow-up observations of GRB 190114C, the first ever GRB detected with high
significance at TeV photon energies by the MAGIC telescope, conducted with the
East Asia VLBI Network (EAVN) at 22 GHz on three epochs, corresponding to 6, 15
and 32 days after the burst. The derived maps do not show any significant
source above 5 sigma. The inferred upper limits on the GRB 190114C flux density
at 22 GHz are used here to constrain the allowable two-dimensional parameter
space for the afterglow emission. We find that our limits are consistent with
most afterglow parameter combinations proposed so far in the literature. This
is the first effort for the EAVN to search and monitor a radio transient in the
Target of Opportunity mode. In addition to the useful constraints on GRB
190114C radio emission, experience gained from these observations is very
helpful for future routine operation of EAVN transient program.
