  In this paper, we focus on ram-pressure stripping and evaporation of disk
galaxies in and around a cluster. We show that the evolution of the disk
surface density affects the efficiency of ram-pressure stripping of galaxies at
z>~1. We also consider the saturation of thermal conduction in detail and show
that it cannot be ignored at larger radii of a cluster, which makes the
time-scale of the evaporation larger. Both the ram-pressure stripping and
evaporation could affect the evolution of galaxies even around a cluster. In
particular, the observed gradual decline of the star-formation rates of
galaxies in and around clusters could be explained by evaporation without
resorting to speculative strangulation (stripping of warm gas in galactic
halos).
