The self-consistent Hartree-Fock approximation and the deformable jellium model are used to describe the ground state of the two-dimensional electron gas. Improved precision in the calculations allows us to confirm the existence of a stable corrugated state at finite densities. This is strongly corroborated by an extrapolation of our results to the low-density region. A positive bulk modulus is obtained in this region. A comparison with experimental data for the melting point and our model calculation is made and agreement is found within a factor of 2.

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