  In Minkowski geometry the unit ball is a compact convex body $K$ containing
the origin in its interior. The boundary of the body is formed by the unit
vectors. We also have a so-called Minkowski functional to measure the length of
vectors. By changing the origin in the interior of the body we have a smoothly
varying family of Minkowski functionals. This is called the Funk metric. Under
some regularity conditions the Minkowski functionals allow us to measure the
volume (area) of the indicatrix bodies (hypersurfaces). Some homogenity
properties provide the volume and the area to be proportional. The area as the
function of the base point varying in the interior of $K$ is strictly convex
[25]. This is called the area function of the Funk manifold. If the minimum is
attained at the origin then $K$ is said to be balanced. The idea comes from the
generalization of Brickell's theorem [6] for Finsler manifolds with balanced
indicatrices [25]. As a continuation of [25] we are going to investigate
analytic properties and the asymptotic behavior of the area function of a Funk
manifold. We prove that the area function is locally analytic and the area can
be arbitrary large near to the boundary of $K$. Therefore the minimum always
attained at a uniquely determined interior point of $K$. If we apply the result
to the indicatrices of a Finsler manifold point by point then the uniquely
defined minima of the area functions constitute a vector field. We prove that
it is differentiable. Therefore each indicatrix body can be translated in such
a way that the translated body is balanced and we always have an associated
Finsler manifold with balanced indicatrices. Finsler manifolds having balanced
indicatrices represent a class of Finsler spaces such that the so-called
Brickell's conjecture holds [6], see also [25].
