  We give several characterizations of parabolic (quasisuper)- minimizers in a
metric measure space equipped with a doubling measure and supporting a
Poincar\'e inequality. We also prove a version of comparison principle for
super- and subminimizers on parabolic space-time cylinders and a uniqueness
result for minimizers of a boundary value problem. We also give an example
showing that the corresponding results do not hold, in general, for
quasiminimizers even in the Euclidean case.
