Local rigidity, bifurcation, and stability of Hf-hypersurfaces in weighted Killing warped products
Velásquez, Marco Antonio (Universidade Federal de Campina Grande. Departamento de Matemática)
Lima, Henrique F. de (Universidade Federal de Campina Grande. Departamento de Matemática)
Ramalho, Andre F. A. (Universidade Federal de Campina Grande. Departamento de Matemática)

Date:	2021
Abstract:	In a weighted Killing warped product Mn f ×ρR with warping metric h , iM+ρ2 dt, where the warping function ρ is a real positive function defined on Mn and the weighted function f does not depend on the parameter t ∈ R, we use equivariant bifurcation theory in order to establish sufficient conditions that allow us to guarantee the existence of bifurcation instants, or the local rigidity for a family of open sets {Ωγ}γ∈I whose boundaries ∂Ωγ are hypersurfaces with constant weighted mean curvature. For this, we analyze the number of negative eigenvalues of a certain Schrödinger operator and study its evolution. Furthermore, we obtain a characterization of a stable closed hypersurface x: Σn ,→ Mn f ×ρ R with constant weighted mean curvature in terms of the first eigenvalue of the f-Laplacian of Σn.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Publicacions matemàtiques, Vol. 65, Num. 1 (2021) , p. 363-388 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/384462
Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT6512113
DOI: 10.5565/PUBLMAT6512113
DOI: 10.5565/publicacionsmatematiques.v65i1.384462

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