  We prove upper bounds for geodesic periods of automorphic forms over general
rank one locally symmetric spaces. Such periods are integrals of automorphic
forms restricted to special totally geodesic cycles of the ambient manifold and
twisted with automorphic forms on the cycles. The upper bounds are in terms of
the Laplace eigenvalues of the two automorphic forms, and they generalize
previous results for real hyperbolic manifolds to the context of all rank one
locally symmetric spaces.
