Spectral Inequalities of the Laplacian on a Curved Tube With Varying Cross Section

Abstract

Abstract. In this note, we consider a curved tube with varying crosssection 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 [1].