  Motivated by the connection between the first eigenvalue of the
Dirichlet-Laplacian and the torsional rigidity, the aim of this paper is to
find a physically coherent and mathematically interesting new concept for
boundary torsional rigidity, closely related to the Steklov eigenvalue. From a
variational point of view, such a new object corresponds to the sharp constant
for the trace embedding of $W^{1,2}(\Omega)$ into $L^1(\partial\Omega)$. We
obtain various equivalent variational formulations, present some properties of
the state function and obtain some sharp geometric estimates, both for planar
simply connected sets and for convex sets in any dimension.
