Geometriae Dedicata

, Volume 178, Issue 1, pp 21–47 | Cite as

Stability properties and topology at infinity of \(f\)-minimal hypersurfaces

Original Paper


We study stability properties of \(f\)-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry–Émery 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.


\(f\)-minimal hypersurfaces Weighted manifolds Stability Finite index Topology at infinity 

Mathematics Subject Classification

53C42 53C21 



Part of this work was done while we were visiting the Institut Henri Poincaré, Paris. We would like to thank the institute for the warm hospitality. Moreover we are deeply grateful to Stefano Pigola for useful conversations during the preparation of the manuscript. We would also like to thank Marcio Batista and Heudson Mirandola and the anonymous referee for useful comments.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano BicoccaMilanItaly

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