Stability properties and topology at infinity of $$f$$f-minimal hypersurfaces

By Debora Impera, Michele Rimoldi. 2013

67 citations recorded by the source corpus.

We study stability properties of $$f$$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 $$f$$f-minimal hypersurfaces. On the way, we prove a new comparison result in weighted geometry and we provide a general weighted $$L^1$$L1-Sobolev inequality for hypersurfaces in Cartan–Hadamard weighted manifolds, satisfying suitable restrictions on the weight function.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ee9b69474d636948f14a863614b012c2c2b238c1