  Solving the Plateau problem means to find the surface with minimal area among
all surfaces with a given boundary. Part of the problem actually consists of
giving a suitable definition to the notions of 'surface', 'area' and
'boundary'. The sliding boundary condition has been introduced by David in
order to study the boundary regularity of minimal sets. In order to do that an
important step is to know the list of minimal boundary cones, that is to say
tangent cones on boundary points of minimal surfaces. In this paper we focus on
cones contained in an half-space and whose boundary can slide along the
bounding hyperplane. After giving a classification of one-dimensional minimal
cones in the half-plane we provide four new two-dimensional minimal cones in
the three-dimensional half space (which cannot be obtained as the Cartesian
product of the real line with one of the previous cones).
