  The electric capacity of a conductor in the 3-dimensional Euclidean space
$R^3 $ is defined as a ratio of a given positive charge on the conductor to the
value of potential on the surface. This definition of the capacity is
independent of the given charge. The capacity of a set as a mathematical notion
was defined first by N. Wiener (1924) and was developed by O. Forstman, C. J.
de La Vallee Poussin, and several other French mathematicians in connection
with potential theory. This paper develops the theory of conformal invariants
for Finsler manifolds. More precisely we prove: The capacity of a compact set
and the capacity of the condenser of two closed sets are conformally invariant.
By mean of the notion of capacity, we construct and study four conformal
invariant functions $ \rho$, $ \nu$, $\mu$ and $\lambda$ which have
similarities with the classical invariants on $S^n$, $ R^n $ or $H^n$. Their
properties and especially their continuity are efficient tools for solving some
problems of conformal geometry in the large.
