  The equilibrium shapes of InAs quantum dots (i.e., dislocation-free, strained
islands with sizes >= 10,000 atoms) grown on a GaAs (001) substrate are studied
using a hybrid approach which combines density functional theory (DFT)
calculations of microscopic parameters, surface energies, and surface stresses
with elasticity theory for the long-range strain fields and strain relaxations.
In particular we report DFT calculations of the surface stresses and analyze
the influence of the strain on the surface energies of the various facets of
the quantum dot. The surface stresses have been neglected in previous studies.
Furthermore, the influence of edge energies on the island shapes is briefly
discussed. From the knowledge of the equilibrium shape of these islands, we
address the question whether experimentally observed quantum dots correspond to
thermal equilibrium structures or if they are a result of the growth kinetics.
