  We study the structure of the higher-curvature gravitational densities that
are induced from holographic renormalization in AdS$_{d+1}$. In a braneworld
construction, such densities define a d-dimensional higher-curvature
gravitational theory on the brane, which in turn is dual to a (d-1)-dimensional
CFT living at its boundary. We show that this CFT$_{d-1}$ satisfies a
holographic c-theorem in general dimensions (different than the g-theorem of
holographic boundary CFTs), since at each and every order the higher-curvature
densities satisfy c-theorems on their own. We find that, in these densities,
the terms that affect the monotonicity of the holographic c-function are
algebraic in the curvature, and do not involve covariant derivatives of the
Riemann tensor. We examine various other features of the holographically
induced higher-curvature densities, such as the presence of reduced-order
traced equations, and their connection to Born-Infeld-type gravitational
Lagrangians.
