A spectral isoperimetric inequality for cones

DOI10.1007/s11005-016-0917-8zbMath1360.35207arXiv1512.01970OpenAlexW2192399959MaRDI QIDQ524128

Pavel Exner, Vladimir Lotoreichik

Publication date: 25 April 2017

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.01970

zbMATH Keywords

Schrödinger operatorisoperimetric inequalityconical surface\(\delta \)-interactionexistence of bound states

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (11)

Discrete spectrum of interactions concentrated near conical surfaces ⋮ An optimization problem for finite point interaction families ⋮ Spectral asymptotics for \(\delta\)-interactions on sharp cones ⋮ Upper and lower bounds for the Hilbert-Schmidt norm of a potential operator ⋮ Spectral isoperimetric inequalities for singular interactions on open arcs ⋮ Eigenvalue counting function for Robin Laplacians on conical domains ⋮ Discrete spectrum of Schrödinger operators with potentials concentrated near conical surfaces ⋮ Spectral optimization for singular Schrödinger operators ⋮ Optimization of the lowest eigenvalue for leaky star graphs ⋮ Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones ⋮ Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane

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