Quasiconformal Harmonic mappings and the curvature of the boundary

We estimate the Jacobian of harmonic mapping of the unit disk onto a smooth and convex Jordan domain via the boundary function and the boundary curvature of the image domain. By using this result we make some asymptotically sharp estimates of constant of quasiconformality for harmonic diffeomorphisms between the unit disk and the convex domains via their boundary mappings.