  The volume of the region inside the bulk Ryu-Takayanagi surface is a
codimension-one object, and a natural generalization of holographic complexity
to the case of subregions in the boundary QFT. We focus on time-independent
geometries, and study the properties of this volume in various circumstances.
We derive a formula for computing the volume for a strip entangling surface and
a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the
volume exhibits non-monotonic behaviour as a function of the size of the
entangling region (unlike the behaviour of the entanglement entropy in this
setup, which is monotonic). For setups in which the holographic entanglement
entropy exhibits transitions in the bulk, such as global AdS black hole,
geometries dual to confining theories and disjoint entangling surfaces, the
corresponding volume exhibits a discontinuous finite jump at the transition
point (and so do the volumes of the corresponding entanglement wedges). We
compute this volume discontinuity in several examples. Lastly, we compute the
codim-zero volume and the bulk action of the entanglement wedge for the case of
a sphere entangling surface and pure AdS geometry.
