Abstract
Two issues are treated in this talk: (i) the generic fact that if a fermionic superfluid in the BCS regime overflows from a narrow container into a much wider one, pairing is much suppressed at the overflow point. Physical examples in cold atoms, neutron stars and nuclei where this feature may play an important role are discussed. (ii) A Thomas-Fermi (TF)approach to inhomogeneous superfluid Fermi-systems is presented and shown that it works well in cases where the Local Density Approximation (LDA) breaks down.
