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In this paper, we focus on ram-pressure stripping and evaporation of diskgalaxies in and around a cluster. We show that the evolution of the disksurface density affects the efficiency of ram-pressure stripping of galaxies atz>~1. We also consider the saturation of thermal conduction in detail and showthat it cannot be ignored at larger radii of a cluster, which makes thetime-scale of the evaporation larger. Both the ram-pressure stripping andevaporation could affect the evolution of galaxies even around a cluster. Inparticular, the observed gradual decline of the star-formation rates ofgalaxies in and around clusters could be explained by evaporation withoutresorting to speculative strangulation (stripping of warm gas in galactichalos).Comment: Changes made to match the version to be published in PAS

The Evolution of Galaxies in and around Clusters at High-Redshift