  In this paper we consider open billiard flows in Euclidean spaces with C^1
(un)stable laminations over their non-wandering sets. We show that for such
billiard flows the standard symplectic form satisfies a specific non-degeneracy
condition over the non-wandering set. This allows to use some previous general
results and obtain Dolgopyat type estimates for spectra of Ruelle transfer
operators under simpler conditions. We also describe a class of open billiard
flows in Euclidean spaces satisfying a certain pinching condition, which in
turn implies that the (un)stable laminations over the non-wandering set are
C^1.
