  We consider the Laplacian in curved tubes of arbitrary cross-section rotating
together with the Frenet frame along curves in Euclidean spaces of arbitrary
dimension, subject to Dirichlet boundary conditions on the cylindrical surface
and Neumann conditions at the ends of the tube. We prove that the spectral
threshold of the Laplacian is estimated from below by the lowest eigenvalue of
the Dirichlet Laplacian in a torus determined by the geometry of the tube.
