The response of low-dimensional solid objects combines geometry and physics in
unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous
in nature and technology. Here we provide a consequence of this confluence of geometry and physics
in tubular structures: our analysis shows that the persistence of a localized pinch in an elastic pipe
whose effect decays as an oscillatory exponential with a persistence length that diverges as the
thickness of the tube vanishes, which we confirm using simulations and simple experiments. The
result is more a consequence of geometry than material properties, and is thus equally applicable
to carbon nanotubes as it is to oil pipelines.