  We study the holographic entanglement entropy of spatial regions having
arbitrary shapes in the AdS4/BCFT3 correspondence with static gravitational
backgrounds, focusing on the subleading term with respect to the area law term
in its expansion as the UV cutoff vanishes. An analytic expression depending on
the unit vector normal to the minimal area surface anchored to the entangling
curve is obtained. When the bulk spacetime is a part of AdS4, this formula
becomes the Willmore functional with a proper boundary term evaluated on the
minimal surface viewed as a submanifold of a three dimensional flat Euclidean
space with boundary. For some smooth domains, the analytic expressions of the
finite term are reproduced, including the case of a disk disjoint from a
boundary which is either flat or circular. When the spatial region contains
corners adjacent to the boundary, the subleading term is a logarithmic
divergence whose coefficient is determined by a corner function that is known
analytically, and this result is also recovered. A numerical approach is
employed to construct extremal surfaces anchored to entangling curves with
arbitrary shapes. This analysis is used both to check some analytic results and
to find numerically the finite term of the holographic entanglement entropy for
some ellipses at finite distance from a flat boundary.
