Works citing   [Ann. H. Poincare 2 (2001), pp. 553-572]

1. T. Tsurumi and M. Wadati:
   Ground state properties of a toroidally trapped Bose-Einstein condensate,
   J. Phys. Soc. Japan 70 (2001), pp. 1512-1518.
   
   
2. A. Aslanyan and E. B. Davies:
   Separation of variables in deformed cylinders,
   J. Comput. Phys. 174 (2001), no. 1, pp. 327-344.
   
   
3. T. Ekholm and H. Kovarik:
   Stability of the magnetic Schrodinger operator in a waveguide,
   Commun. in Partial Differential Equations 30 (2005), no. 4-6, pp. 539-565.
   
   
4. C. Lin and Z. Lu:
   Existence of bound states for layers built over hypersurfaces in $R^{n+1}$,
   J. Funct. Anal. 244 (2007), 1-25.
   
   
5. V. V. Grushin:
   Asymptotic behavior of eigenvalues of the Laplace operator in infinite cylinders perturbed by transverse extensions,
   Math. Notes 81 (2007), 291-296.
   
   
6. H. Kovarik and A. Sacchetti:
   Resonances in twisted quantum waveguides,
   J. Phys. A: Math. Theor. 40 (2007), 8371-8384.
   
   
7. V. V. Grushin:
   Asymptotic behavior of the eigenvalues of the Schrodinger operator in thin closed tubes,
   Math. Notes 83 (2008), 463-477.
   
   
8. H. Kovarik and S. Vugalter:
   Estimates on trapped modes in deformed quantum layers,
   J. Math. Anal. Appl. 345 (2008), 566-572.
   
   
9. M. D. Malykh:
   On the emptiness criteria for the discrete spectrum of the Dirichlet problem for the equation Delta nu plus lambda nu=0,
   Comp. Math. Math. Phys. 49 (2009), 279-283.
   
   
10. V. V. Grushin:
    Asymptotic behavior of eigenvalues of the Laplace operator in thin infinite tubes,
    Math. Notes 85 (2009), 661-673.
    
    
11. S. A. Nazarov:
    Trapped modes in a T-shaped waveguide,
    Acoust. Phys. 56 (2010), 1004-1015.
    
    
12. S. A. Nazarov:
    Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide,
    Theor. Math. Phys. 167 (2011), 606-627.
    
    
13. S. A. Nazarov:
    Asymptotic formulas for trapped modes and for eigenvalues below the threshold of the continuous spectrum of a waveguide with a thin screening barrier,
    St. Petersburg Math. J. 23 (2012), 571-601.
    
    
14. S. A. Nazarov:
    On the spectrum of the laplace operator on the infinite dirichlet ladder,
    St. Petersburg Math. J. 23 (2012), 1023-1045.
    
    
15. G. Cardone, S. A. Nazarov and K. Ruotsalainen:
    Bound states of a converging quantum waveguide,
    ESAIM Math. Model. Numer. Anal. 47 (2013), 305-315.
    
    
16. G. Cardone:
    Asymptotic Analysis of an Eigenvalue in the Discrete Spectrum of a Quantum Waveguide,
    11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2013), AIP Conference Proceedings 1558 (2013), 1809-1812.
    
    
17. S. Kondej:
    Schrodinger operator with a strong varying interaction on a curve in R^2,
    J. Math. Phys. 54 (2013) 093511.
    
    
18. J. Stockhofe and P. Schmelcher:
    Nonadiabatic couplings and gauge-theoretical structure of curved quantum waveguides,
    Phys. Rev. A 89 (2014), 033630.
    
    
19. S. A. Nazarov, K. Ruotsalainen and P. Uusitalo:
    The Y-junction of quantum waveguides,
    ZAMM - Journal of Applied Mathematics and Mechanics 89 (2014), 477-486.
    
    
20. R. Novak:
    Bound states in waveguides with complex Robin boundary conditions,
    Asympt. Anal. 96 (2016) 251-281.
    
    
21. S. A. Nazarov, K. M. Ruotsalainen and M. Silvola:
    Trapped Modes in Piezoelectric and Elastic Waveguides,
    J. Elasticity 124 (2016) 193-223.
    
    
22. B. M. Brown, V. Hoang, M. Plum, M. Radosz and I. Wood:
    Gap localization of TE-modes by arbitrarily weak defects,
    J. London Math. Soc. (2) 95 (2017) 942-962.
    
    
23. I. Y. Popov and A. I. Popov:
    Line with attached segment as a model of Helmholtz resonator: Resonant states completeness,
    Journal of King Saud University Science 29 (2017) 133-136.
    
    
24. A. I. Popov, I. Y. Popov and D. A. Gerasimov:
    Resonance State Completeness Problem for Quantum Graph,
    Proceedings Of The International Conference On Numerical Analysis And Applied Mathematics 2016 (ICNAAM-2016) 1863 (2017) UNSP 390002-1.
    
    
25. P. Amore, J. P. Boyd and F. M. Fernandez:
    Bound States In Weakly Deformed Waveguides: Numerical Versus Analytical Results,
    ANZIAM Journal 59 (2017) 200-214.
    
    
26. A. A. Verri:
    Dirichlet Laplacian in a thin twisted strip,
    Int. J. Math. 30 (2019) 1950006.
    
    
27. S. Kim:
    Application of a complete radiation boundary condition for the Helmholtz equation in locally perturbed waveguides,
    J. Comput. Appl. Math. 367 (2020) UNSP 112458.