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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...
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