  In this article, we investigate some geometric inequalities for
quasi-Einstein manifolds. We use the generalized Reilly's formulas by Qiu-Xia
and Li-Xia to establish new boundary estimates and an isoperimetric type
inequality for compact quasi-Einstein manifolds with boundary. Boundary
estimates in terms of the first eigenvalue of the Jacobi operator and the
Hawking mass are also established. In particular, we present a Heintze-Karcher
type inequality for a compact domain on a quasi-Einstein manifold.
