  We study analytically how noninteracting weakly active particles, for which
passive Brownian diffusion cannot be neglected and activity can be treated
perturbatively, distribute and behave near boundaries in various geometries. In
particular, we develop a perturbative approach for the model of active
particles driven by an exponentially correlated random force (active
Ornstein-Uhlenbeck particles). This approach involves a relatively simple
expansion of the distribution in powers of the P\'{e}clet number and in terms
of Hermite polynomials. We use this approach to cleanly formulate boundary
conditions, which allows us to study weakly active particles in several
geometries: confinement by a single wall or between two walls in 1D,
confinement in a circular or wedge-shaped region in 2D, motion near a
corrugated boundary, and finally absorption onto a sphere. We consider how
quantities such as the density, pressure, and flow of the active particles
change as we gradually increase the activity away from a purely passive system.
These results for the limit of weak activity help us gain insight into how
active particles behave in the presence of various types of boundaries.
