Asymptotic spectrum for the Dirichlet Laplacian in thin deformed tubes with scaled geometry
César R. de Oliveira, Alessandra A. Verri · Journal of Physics A Mathematical and Theoretical · 2012
It is known that geometric properties do not play a role in the asymptotics of the eigenvalues of the Laplacian restricted to thin Dirichlet deformed tubular regions. In this work it is shown that, by properly scaling the geometric properties of the tubes, a limit where the geometry is on equal footing with the deformation function is obtained; such a result gives an indication of how subtle the confining limits can be.