\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
% \MRhref is called by the amsart/book/proc definition of \MR.
\providecommand{\MRhref}[2]{%
  \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
}
\providecommand{\href}[2]{#2}
\begin{thebibliography}{PPW56}

\bibitem[AB91]{Ashbaugh-Benguria_1991}
M.~S. Ashbaugh and R.~D. Benguria, \emph{Proof of the
  {P}ayne-{P}{\'o}lya-{W}einberger conjecture}, Bull. Amer. Math. Soc. (N.S.)
  \textbf{25} (1991), no.~1, 19--29.

\bibitem[AB92]{Ashbaugh-Benguria_1992}
\bysame, \emph{A second proof of the {P}ayne-{P}{\'o}lya-{W}einberger
  conjecture}, Comm. Math. Phys. \textbf{147} (1992), no.~1, 181--190.

\bibitem[AE90]{AE}
M.~S. Ashbaugh and P.~Exner, \emph{Lower bounds to bound state energies in bent
  tubes}, Phys. Lett. A~ \textbf{150} (1990), no.~3,4, 183--186.

\bibitem[CDFK]{ChDFK}
B.~Chenaud, P.~Duclos, P.~Freitas, and D.~Krej\v{c}i\v{r}\'{\i}k,
  \emph{Geometrically induced discrete spectrum in curved tubes}, submitted;
  preprint available.

\bibitem[DE95]{DE}
P.~Duclos and P.~Exner, \emph{{C}urvature-induced bound states in quantum
  waveguides in two and three dimensions}, Rev. Math. Phys. \textbf{7} (1995),
  73--102.

\bibitem[E{\v S}89]{ES}
P.~Exner and P.~{\v S}eba, \emph{Bound states in curved quantum waveguides},
  J.~Math.~Phys. \textbf{30} (1989), 2574--2580.

\bibitem[EW01]{EW}
P.~Exner and T.~Weidl, \emph{{L}ieb-{T}hirring inequalities on trapped modes in
  quantum wires}, Proceedings of the XIIIth International Congress on
  Mathematical Physics (London 2000), Int. Press, Boston, MA, 2001,
  pp.~437--443.

\bibitem[GJ92]{GJ}
J.~Goldstone and R.~L. Jaffe, \emph{Bound states in twisting tubes}, Phys. Rev.
  B~ \textbf{45} (1992), 14100--14107.

\bibitem[Hen03]{Henrot_2003}
A.~Henrot, \emph{Minimization problems for eigenvalues of the {L}aplacian},
  Journal of Evolution Equations \textbf{3} (2003), 443--461.

\bibitem[Hur00]{Hurt}
N.~E. Hurt, \emph{Mathematical physics of quantum wires and devices}, Kluwer,
  Dordrecht, 2000.

\bibitem[KK]{KKriz}
D.~Krej\v{c}i\v{r}\'{\i}k and J.~K\v{r}\'{\i}\v{z}, \emph{On the spectrum of
  curved quantum waveguides}, submitted; preprint on [\textsf{mp\_arc 03-264}]
  or [math-ph/0306008].

\bibitem[Kli78]{Kli}
W.~Klingenberg, \emph{A course in differential geometry}, Springer-Verlag, New
  York, 1978.

\bibitem[Lau98]{Laugesen1}
R.~S. Laugesen, \emph{Eigenvalues of the {L}aplacian on inhomogeneous
  membranes}, Amer. J.~Math. \textbf{120} (1998), 305--344.

\bibitem[LCM99]{LCM}
J.~T. Londergan, J.~P. Carini, and D.~P. Murdock, \emph{Binding and scattering
  in two-dimensional systems}, LNP, vol. m60, Springer, Berlin, 1999.

\bibitem[PPW55]{PPW1}
L.~E. Payne, G.~P{\'o}lya, and H.~F. Weinberger, \emph{Sur le quotient de deux
  fr\'equences propres cons\'ecutives}, C.~R. Acad. Sci. Paris \textbf{241}
  (1955), 917--919.

\bibitem[PPW56]{PPW2}
\bysame, \emph{On the ratio of consecutive eigenvalues}, J.~Math. Phys.
  \textbf{35} (1956), 289--298.

\bibitem[RB95]{RB}
W.~Renger and W.~Bulla, \emph{Existence of bound states in quantum waveguides
  under weak conditions}, Lett.~Math.~Phys. \textbf{35} (1995), 1--12.

\bibitem[RS72]{RS1}
M.~Reed and B.~Simon, \emph{Methods of modern mathematical physics,
  {I}.~{F}unctional analysis}, Academic Press, New York, 1972.

\bibitem[Spi79]{Spivak2}
M.~Spivak, \emph{A comprehensive introduction to differential geometry},
  vol.~II, Publish or Perish, Houston, Texas, 1979.

\end{thebibliography}
