2017/01/02 by Hilário Alencar, Alencar, Hilário, Adina Rocha +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C42 #msc:58E30 #msc:58J50
paper · pdf · doi:10.48550/arxiv.1701.00373
arxiv created 2017/01/02 · arxiv updated 2017/01/03
In this paper, we prove that a noncompact complete hypersurface with finite weighted volume, weighted mean curvature vector bounded in norm, and isometrically immersed in a complete weighted manifold is proper. In addition, we obtain an estimate for f-stability index of a constant weighted mean curvature hypersurface with finite weighted volume and isometrically immersed in a shrinking gradient Ricci soliton that admits at least one parallel field globally defined. For such hypersurface, we still give a necessary condition for equality to be achieved in the estimate obtained.