We present a theoretical interpretation of a recent experiment presented in
ref. \cite{Zwierlein06} on the density profile of Fermi gases with unbalanced
spin populations. We show that in the regime of strong interaction, the
boundaries of the three phases observed in \cite{Zwierlein06} can be
characterized by two dimensionless numbers η_α and η_β.
Using a combination of a variational treatment and a study of the experimental
results, we infer rather precise bounds for these two parameters.Comment: 4 pages, 2 figure