A class of rotationally symmetric quantum layers of dimension 4

TL;DR

This paper proves the existence of discrete spectral values below the essential spectrum for the Dirichlet Laplacian on certain 4-dimensional rotationally symmetric quantum layers, highlighting advantages over previous higher-dimensional results.

Contribution

It establishes new spectral existence results for quantum layers over spherically symmetric hypersurfaces in four dimensions, extending prior work to this specific geometric setting.

Findings

Discrete spectrum exists below the essential spectrum under geometric conditions

Results are independent of higher-dimensional quantum layer findings

Main theorem applies to quantum layers over spherically symmetric hypersurfaces in R4

Abstract

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 the Euclidean space R4. 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.