Trapped fermionic clouds distorted from the trap shape due to many-body effects.

We present a general approach for describing trapped Fermi gases, when the cloud shape is distorted with respect to the trap shape. Our approach provides a consistent way to explore physics beyond the local density approximation, if this is necessary due to the distortion. We illustrate this by analyzing in detail experimentally observed distortions in a trapped imbalanced Fermi mixture. In particular, we demonstrate in that case dramatic deviations from ellipsoidal cloud shapes arising from the competition between surface and bulk energies.