On Geometric Quantum Confinement in Grushin-type Manifolds
arXiv:1809.06805 · doi:10.1007/s00033-019-1203-2
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.
16 pages, 2 figures