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We present a general approach for calculating densities and other localquantities of trapped Fermi gases, when the cloud shape is distorted withrespect to the trap shape due to global energy considerations. Our approachprovides a consistent way to explore physics beyond the local densityapproximation, if this is necessary due to the distortion. We illustrate thisby analyzing in detail experimentally observed distortions in an imbalancedFermi mixture in an elongated trap. In particular, we demonstrate in that casedramatic deviations from ellipsoidal cloud shapes arising from the competitionbetween surface and bulk energies.Comment: 4+ pages, 3 figures. Formalism for distorted trapped fermi systems +  treatment of polarized fermion experiments. Version 2: slightly shortened,  published versio

Trapped Fermionic Clouds Distorted from the Trap Shape due to Many-Body Effects