A class of rotationally symmetric quantum layers of dimension 4

Under several geometric conditions imposed below, the existence of the discrete spectrum below the essential spectrum is shown for the Dirichlet Laplacian on the quantum layer built over a spherically symmetric hypersurface with a pole embedded in R 4 . At the end of this paper, we also show the advantage and independence of our main result comparing with those existent results for higher dimensional quantum layers or quantum tubes.