  The zero-temperature linear response conductance through an interacting
mesoscopic region attached to noninteracting leads is investigated. We present
a set of formulas expressing the conductance in terms of the ground-state
energy of an auxiliary system, namely a ring threaded by a magnetic flux and
containing the correlated electron region. We prove that the formalism is exact
if the ground state of the system is a Fermi liquid. We show that in such
systems the ground-state energy is a universal function of the magnetic flux,
where the conductance is the relevant parameter. The method is illustrated with
results for the transport through an interacting quantum dot and a simple
Aharonov-Bohm ring with Kondo-Fano resonance physics.
