We study stability properties of -minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-A parts per thousand mery 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 -minimal hypersurfaces. On the way, we prove a new comparison result in weighted geometry and we provide a general weighted -Sobolev inequality for hypersurfaces in Cartan-Hadamard weighted manifolds, satisfying suitable restrictions on the weight function

Impera, D., Rimoldi, M. (2014). Stability properties and topology at infinity of f-minimal hypersurfaces. GEOMETRIAE DEDICATA, 178(1), 21-47 [10.1007/s10711-014-9999-6].

Stability properties and topology at infinity of f-minimal hypersurfaces

IMPERA, DEBORA;RIMOLDI, MICHELE
2014

Abstract

We study stability properties of -minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-A parts per thousand mery 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 -minimal hypersurfaces. On the way, we prove a new comparison result in weighted geometry and we provide a general weighted -Sobolev inequality for hypersurfaces in Cartan-Hadamard weighted manifolds, satisfying suitable restrictions on the weight function
Articolo in rivista - Articolo scientifico
f-minimal hypersurfaces; weighted manifolds; stability ; finite index; topology at infinity
English
2014
178
1
21
47
none
Impera, D., Rimoldi, M. (2014). Stability properties and topology at infinity of f-minimal hypersurfaces. GEOMETRIAE DEDICATA, 178(1), 21-47 [10.1007/s10711-014-9999-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/61952
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