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On Geometric Quantum Confinement in Grushin-type Manifolds (1809.06805v2)
Published 18 Sep 2018 in math.DG, math-ph, math.MP, and math.SP
Abstract: We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.