  Let $(M,\bar{g}, e^{-f}d\mu)$ be a complete metric measure space with
Bakry-\'Emery Ricci curvature bounded below by a positive constant. We prove
that, in $M$, there is no complete two-sided $L_f$-stable immersed $f$-minimal
hypersurface with finite weighted volume. Further, if $M$ is a 3-manifold, we
prove a smooth compactness theorem for the space of complete embedded
$f$-minimal surfaces in $M$ with the uniform upper bounds of genus and weighted
volume, which generalizes the compactness theorem for complete self-shrinkers
in $\mathbb{R}^3$ by Colding-Minicozzi.
