A class of rotationally symmetric quantum layers of dimension 4
Differential Geometry
2013-01-29 v4 Spectral Theory
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.
Keywords
Cite
@article{arxiv.1203.5465,
title = {A class of rotationally symmetric quantum layers of dimension 4},
author = {Jing Mao},
journal= {arXiv preprint arXiv:1203.5465},
year = {2013}
}
Comments
12 pages. A slight different version of this paper has appeared in J. Math. Anal. Appl