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.

Stability properties and topology at infinity of f-minimal hypersurfaces / Impera, Debora; Rimoldi, Michele. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 178:1(2015), pp. 21-47. [10.1007/s10711-014-9999-6]

Stability properties and topology at infinity of f-minimal hypersurfaces

Impera, Debora;RIMOLDI, MICHELE
2015

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2690993