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We construct and study the intrinsic sub-Laplacian, defined outside the setof characteristic points, for a smooth hypersurface embedded in a contactsub-Riemannian manifold. We prove that, away from characteristic points, theintrinsic sub-Laplacian arises as the limit of Laplace-Beltrami operators builtby means of Riemannian approximations to the sub-Riemannian structure using theReeb vector field. We carefully analyse three families of model cases for thissetting obtained by considering canonical hypersurfaces embedded in modelspaces for contact sub-Riemannian manifolds. In these model cases, we show thatthe intrinsic sub-Laplacian is stochastically complete and in particular, thatthe stochastic process induced by the intrinsic sub-Laplacian almost surelydoes not hit characteristic points.

Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold