  We study the adhesion of an elastic sheet on a rigid spherical substrate.
Gauss'Theorema Egregium shows that this operation necessarily generates metric
distortions (i.e. stretching) as well as bending. As a result, a large variety
of contact patterns ranging from simple disks to complex branched shapes are
observed as a function of both geometrical and material properties. We describe
these different morphologies as a function of two non-dimensional parameters
comparing respectively bending and stretching energies to adhesion. A complete
configuration diagram is finally proposed.
