Singularities and nonhyperbolic manifolds do not coincide

We consider the billiard flow of elastically colliding hard balls on the flat $\nu$-torus ($\nu \ge 2$), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai Ergodic Hypothesis.