  We discuss the response of thin cylindrical tubes to small indentations. The
stretching-free embedding of these surfaces is completely determined by the
embedding of one edge curve, thus reducing their bending response to an
effectively one dimensional problem. We obtain that in general thin cylindrical
tubes will bend non-uniformly in response to an indentation normal to their
surface. As a consequence, their local bending stiffness, as measured by
indenting at various locations along their axis, is predicted to peak at the
center and decrease by a universal factor of 4 at either end of the tube. This
characteristic spatial profile of the bending stiffness variation allows a
direct determination of the bending modulus of very thin tubes that are shorter
than their pinch persistence length, $l_{p}\propto R^{3/2}/t^{1/2}$, where $R$
is the tube diameter and $t$ its wall thickness. We compare our results with
experiments performed on rolled-up stainless steel sheets.

Soft Condensed Matter