  To investigate the rigidity and flexibility of Lagrangian cobordisms between
Legendrian submanifolds, we investigate the minimal length of such a cobordism,
which is a $1$-dimensional measurement of the non-cylindrical portion of the
cobordism. Our primary tool is a set of real-valued capacities for a Legendrian
submanifold, which are derived from a filtered version of Legendrian Contact
Homology. Relationships between capacities of Legendrians at the ends of a
Lagrangian cobordism yield lower bounds on the length of the cobordism. We
apply the capacities to Lagrangian cobordisms realizing vertical dilations
(which may be arbitrarily short) and contractions (whose lengths are bounded
below). We also study the interaction between length and the linking of
multiple cobordisms as well as the lengths of cobordisms derived from
non-trivial loops of Legendrian isotopies.
