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It is shown that the absolute value of the persistent current in a systemwith toroidal geometry is rigorously less than or equal to $e \hbar N /4 \pi mr_0^2$, where $N$ is the number of electrons, and $r_0^{-2} = \langler_i^{-2}\rangle$ is the equilibrium average of the inverse of the square of thedistance of an electron from an axis threading the torus. This result is validin three and two dimensions for arbitrary interactions, impurity potentials,and magnetic fields.Comment: 10 pages + 1 figure available by request, Revte

Rigorous upper bound for the persistent current in systems with toroidal geometry