  We study Markov processes conditioned so that their local time must grow
slower than a prescribed function. Building upon recent work on Brownian motion
with constrained local time in [5] and [33], we study transience and recurrence
for a broad class of Markov processes.
  In order to understand the distribution of the local time, we determine the
distribution of a non-decreasing L\'evy process (the inverse local time)
conditioned to remain above a given level which varies in time. We study a
time-dependent region, in contrast to previous works in which a process is
conditioned to remain in a fixed region (e.g. [21,27]), so we must study
boundary crossing probabilities for a family of curves, and thus obtain uniform
asymptotics for such a family.
  Main results include necessary and sufficient conditions for transience or
recurrence of the conditioned Markov process. We will explicitly determine the
distribution of the inverse local time for the conditioned process, and in the
transient case, we explicitly determine the law of the conditioned Markov
process. In the recurrent case, we characterise the "entropic repulsion
envelope" via necessary and sufficient conditions.
