A class of rotationally symmetric quantum layers of dimension 4

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.

arXiv comment12 pages. A slight different version of this paper has appeared in J. Math. Anal. Appl

References in corpus (2)

• Bound States in Curved Quantum Layers
• Open manifold with nonnegative Ricci curvature and collapsing volume

Cited by in corpus (4)

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• Schrödinger operators with $\delta$-interactions supported on conical surfaces
• Monotonicity of the first eigenvalue of the Laplace and the p-Laplace operators under a forced mean curvature flow
• Geometry and topology of manifolds with integral radial curvature bounds