Communications of the
Korean Mathematical Society CKMS

In this note, we consider a curved tube with varying cross-section formed by rotating open bounded Euclidean domains with respect to a reference curve, and successfully give a lower bound to the threshold of the Laplacian on the tube, subject to Dirichlet boundary conditions on the surface and Neumann conditions at the ends of the tube. This generalizes the corresponding result in \cite{ppd}.

Keywords: spectral threshold, curved tubes, cross section, Bessel function

MSC numbers: 35P15, 58C40