References
- Duclos P , Exner P . Curvature-induced bound states in quantum waveguides in two and three dimensions. Rev Math Phys. 1995;7:73–102.
- Exner P , Ichinose T . Geometrically induced spectrum in curved leaky wires. J Phys A: Math Gen. 2001;34:1439–1450.
- Exner P , Šeba P . Bound states in curved quantum waveguides. J Math Phys. 1989;30:2574–2580.
- Goldstone J , Jaffe RL . Bound states in twisting tubes. Phys Rev. 1992;B45:14100–14107.
- Carron G , Exner P , Krejčiřík D . Topologically non-trivial quantum layers. J Math Phys. 2004;45:774–784.
- Duclos P , Exner P , Krejčiřík D . Bound states in curved quantum layers. Commun Math Phys. 2001;223:13–28.
- Exner P , Tater M . Spectrum of Dirichlet Laplacian in a conical layer. J Phys A: Math Theor. 2010;43:474023.
- Dauge M , Ourmières-Bonafos T , Raymond N . Spectral asymptotics of the Dirichlet Laplacian in a conical layer. Commun Pure Appl Anal. 2015;14:1239–1258.
- Behrndt J , Exner P , Lotoreichik V . Schrödinger operators with δ-interactions supported on conical surfaces. J Phys A: Math Theor. 2014;47:355202.
- Lotoreichik V , Ourmières-Bonafos T . On the bound states of Schrödinger operators with δ-interactions on conical surfaces. Commun PDE. 2016;41:999–1028.
- Albeverio S , Gesztesy F , Høegh-Krohn R , et al . Solvable models in quantum mechanics. 2nd ed. Providence, RI: With an Appendix by P. Exner. AMS Chelsea Publishing; 2005.
- Exner P , Kovařík H . Quantum waveguides. Theoretical and mathematical physics. Springer; 2015. Vol. 22,
- Exner P . Leaky quantum graphs: a review. In: Exner P , Keating JP , Kuchment P , Sunada T and Teplyaev A , editors. Analysis of graphs and its applications. Providence (RI): American Mathematical Society; 2008 (Vol. 77, p. 523–564. Proceedings of symposia in pure mathematics).
- Bruneau V , Popoff N . On the negative spectrum of the Robin Laplacian in corner domains. Anal PDE. 2016;9:1259–1283.
- Exner P , Lotoreichik V . A spectral isoperimetric inequality for cones. Lett Math Phys. 2017;107:717–732.
- Bruneau V , Pankrashkin K , Popoff N . Eigenvalue counting function for Robin Laplacians on conical domains. J Geom Anal. 2017. DOI:10.1007/s12220-017-9813-4.
- Krejčiřík D , Lotoreichik V , Ourmières-Bonafos T . Spectral transitions for Aharonov--Bohm Laplacians on conical layers. Preprint arXiv:1607.02454.
- Pankrashkin K . On the discrete spectrum of Robin Laplacians in conical domains. Math Model Nat Phenom. 2016;11(2):100–110.
- Rado T . The isoperimetric inequality on the sphere. Am J Math. 1935;57:765–770.
- Dittrich J , Exner P , Kühn C , et al . On eigenvalue asymptotics for strong δ-interactions supported by surfaces with boundaries. Asymptot Anal. 2016;97:1–25.
- Exner P , Pankrashkin K . Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc. Commun PDE. 2014;39:193–212.
- Kuchment P . Quantum graphs I. Some basic structures. Waves Random Media. 2004;14:S107–S128.
- Exner P , Yoshitomi K . Asymptotics of eigenvalues of the Schrödinger operator with a strong δ-interaction on a loop. J Geom Phys. 2002;41:344–358.
- Kirsch W , Simon B . Corrections to the classical behavior of the number of bound states of Schrödinger operators. Ann Phys. 1988;183:122–130.