Stability properties and topology at infinity of f-minimal hypersurfaces

e study stability properties of f–minimal hypersurfaces isometrically immersed in weighted manifolds with non–negative Bakry–Emery Ricci ´ curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li–Tam theory, we investigate the topology at infinity of f–minimal hypersurfaces. On the way, we prove a new comparison result in weighted geometry and we provide a general weighted L 1–Sobolev inequality for hypersurfaces in Cartan– Hadamard weighted manifolds, satisfying suitable restrictions on the weight function.