Stability properties and topology at infinity of f-minimal hypersurfaces

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.

30 pages. Final version: to appear on Geom. Dedicata

References in corpus (3)

• Complete self-shrinkers confined into some regions of the space
• On a classification theorem for self-shrinkers
• Topology of steady and expanding gradient Ricci solitons via f-harmonic maps

Cited by in corpus (4)

• Rigidity results and topology at infinity of translating solitons of the mean curvature flow
• $\varphi$-parabolicity and the uniqueness of spacelike hypersurfaces immersed in a spatially weighted GRW spacetime
• Dirichlet problem for $f$-minimal graphs
• Essential Spectrum of the Weighted Laplacian on Noncompact Manifolds and Applications