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arXiv · 1302.6160

Stability properties and topology at infinity of f-minimal hypersurfaces

Debora Impera·Michele Rimoldi
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Abstract

We 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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Debora Impera, Michele Rimoldi. 2013-02-25. Stability properties and topology at infinity of f-minimal hypersurfaces. https://doi.org/10.1007/s10711-014-9999-6

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