  A comb domain is defined to be the entire complex plain with a collection of
vertical slits, symmetric over the real axis, removed. In this paper, we
consider the question of determining whether the exit time of planar Brownian
motion from such a domain has finite $p$-th moment. This question has been
addressed before in relation to starlike domains, but these previous results do
not apply to comb domains. Our main result is a sufficient condition on the
location of the slits which ensures that the $p$-th moment of the exit time is
finite. Several auxiliary results are also presented, including a construction
of a comb domain whose exit time has infinite $p$-th moment for all $p \geq
1/2$.
