  There has been considerable interest in the possible cosmic string
configurations and Y. Yang has recently derived intriguing obstructions to the
existence of cylindrically symmetric solutions in the Bogomol'nyi critical
phase of the Einstein-Maxwell-Higgs system. In this comment, we would like to
mention some earlier results and recent progress which were not reflected there
but are important in connection with the obstructions he claimed. Some of his
obstructions are not consistent with the ealier results. Also, we give a new
condition stronger than those found before.
