  Recent studies have highlighted the sensitivity of active matter to
boundaries and their geometries. Here we develop a general theory for the
dynamics and statistics of active particles on curved surfaces and illustrate
it on two examples. We first show that active particles moving on a surface
with no ability to probe its curvature only exhibit steady-state
inhomogeneities in the presence of orientational order. We then consider a
strongly confined 3D ideal active gas and compute its steady-state density
distribution in a box of arbitrary convex shape.
