A class of rotationally symmetric quantum layers of dimension 4

Details A class of rotationally symmetric quantum layers of dimension 4 A class of rotationally symmetric quantum layers of dimension 4

2012-03-25

arxiv.org/abs/1203.5465v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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 give examples to show the advantage and independence of our main result comparing with those existent results for higher dimensional quantum layers or quantum tubes.

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