  In this article, we establish a truncated non-integrated defect relation for
meromorphic mappings from an $m$-dimensional complete K\"{a}hler manifold into
$\mathbb P^n(\mathbb C)$ intersecting $q$ hypersurfaces $Q_1,...,Q_q$ in
$k$-subgeneral position of degree $d_i$, i.e., the intersection of any $k+1$
hypersurfaces is emptyset. We will prove that $$
\sum_{i=1}^q\delta_f^{[u-1]}(Q_i)\le (k-n+1)(n+1)+\epsilon+\frac{\rho
u(u-1)}{d}, $$ where $u$ is explicitly estimated and $d$ is the least common
multiple of $d_i'$s. Our result generalizes and improves previous results. In
the last part of this paper we will apply this result to study the distribution
of the Gauss map of minimal surfaces.
