Quantum layers over surfaces ruled outside a compact set

In this paper, we prove that quantum layers over a surface which is ruled outside a compact set, nonplanar but asymptotically flat, admit a ground state for the Dirichlet Laplacian. The work here also represents some technical progress toward resolving the conjecture that a quantum layer over any nonplanar, asymptotically flat surface with integrable Gauss curvature must possess ground state.

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