  In this article we have studied some properties of subharmonic functions in a
strongly symmetric Riemannian manifold with a pole. As a generalization of
polynomial growth of a function we have introduced the notion of polynomial
growth of some degree of a function with respect to a real function and proved
that any non-negative twice differentiable subharmonic functions in an
$n$-dimensional manifold always admit polynomial growth of degree $1$ with
respect to a non-negative real valued subharmonic function on real line. We
have also given a lower bound of the integration of a convex function in a
geodesic ball.
