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Annals of Global Analysis and Geometry

, Volume 53, Issue 4, pp 561–581 | Cite as

Stability and geometric properties of constant weighted mean curvature hypersurfaces in gradient Ricci solitons

  • Hilário Alencar
  • Adina Rocha
Article

Abstract

In this paper, we study stability properties of hypersurfaces with constant weighted mean curvature (CWMC) in gradient Ricci solitons. The CWMC hypersurfaces generalize the f-minimal hypersurfaces and appear naturally in the isoperimetric problems in smooth metric measure spaces. We obtain a result about the relationship between the properness and extrinsic volume growth under the assumption of a limitation for the weighted mean curvature of the immersion. Moreover, we estimate Morse index for CWMC hypersurfaces in terms of the dimension of the space of parallel vector fields restricted to hypersurface.

Keywords

Hypersurface Weighted volume Weighted mean curvature Stability Index 

Mathematics Subject Classification

58J50 53C42 58E30 

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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Instituto de MatemáticaUniversidade Federal de AlagoasMaceióBrazil

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