LAUSR

We consider how m-dimensional Bakry-Émery Ricci curvature affects the geometry of the boundary $$\partial M$$∂M. By using the Reilly’s formula with respect to f-Laplacian, geometric inequalities involving f-mean curvature are obtained. Furthermore, we also achieve the relationship between f-mean curvature of the boundary submanifold and the mean curvature of submanifold $$x:\partial M\rightarrow \mathbb {R}^N(c)$$x:∂M→RN(c) into space form $$\mathbb {R}^N(c)$$RN(c).