Stability properties and topology at infinity of -minimal hypersurfaces

作者：Impera Debora^*; Rimoldi Michele

来源：Geometriae Dedicata, 2015, 178(1): 21-47.

DOI：10.1007/s10711-014-9999-6

• f-minimal hypersurfaces
• Weighted manifolds
• Stability
• Finite index
• Topology at infinity

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.

• 出版日期2015-10