Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds

DOI10.1080/03605302.2015.1095766zbMath1342.35196arXiv1406.6578OpenAlexW1783662855MaRDI QIDQ2810592

Dario Prandi, Marcello Seri, Ugo V. Boscain

Publication date: 3 June 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.6578

zbMATH Keywords

Laplace-Beltrami operatorsub-Riemannian geometrycounting functionAharonov-Bohm effectembedded eigenvaluesWeyl's lawalmost-Riemannian geometryspectral accumulation

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Elliptic equations on manifolds, general theory (58J05) Sub-Riemannian geometry (53C17) Local differential geometry (53Bxx)

Related Items (12)

Null Controllability of the Parabolic Spherical Grushin Equation ⋮ Product formulas and convolutions for Laplace-Beltrami operators on product spaces: beyond the trivial case ⋮ Singular Weyl’s law with Ricci curvature bounded below ⋮ Quantum geometric confinement and dynamical transmission in Grushin cylinder ⋮ From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere ⋮ Mini-workshop: Zero-range and point-like singular perturbations: for a spillover to analysis, PDE and differential geometry. Abstracts from the mini-workshop held October 2--8, 2022 ⋮ Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces ⋮ Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group ⋮ Quantum confinement for the curvature Laplacian \(- \Delta + cK\) on 2D-almost-Riemannian manifolds ⋮ Weyl's law for singular Riemannian manifolds ⋮ Closure of the Laplace-Beltrami operator on 2D almost-Riemannian manifolds and semi-Fredholm properties of differential operators on Lie manifolds ⋮ Quantum particle across Grushin singularity ^*

Uses Software

• DLMF

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