Cekic, M.M.CekicGeorgiev, BogdanBogdanGeorgievMukherjee, M.M.Mukherjee2022-03-062022-03-062020https://publica.fraunhofer.de/handle/publica/26367310.1007/s00220-020-03741-0We study dynamical properties of the billiard flow on convex polyhedra away from a neighbourhood of the non-smooth part of the boundary, called ""pockets"". We prove there are only finitely many immersed periodic tubes missing the pockets and moreover establish a new quantitative estimate for the lengths of such tubes. This extends well-known results in dimension 2. We then apply these dynamical results to prove a quantitative Laplace eigenfunction mass concentration near the pockets of convex polyhedral billiards. As a technical tool for proving our concentration results on irrational polyhedra, we establish a control-theoretic estimate on a product space with an almost-periodic boundary condition. This extends previously known control estimates for periodic boundary conditions, and seems to be of independent interest.en005530006629journal article