Bifurcation and local rigidity of constant second mean curvature hypersurfaces in Riemannian warped products

被引：0

作者：

Velasquez, Marco A. L. ^{[1
]}

Ramalho, Andre F. A. ^{[1
]}

da Silva, Jonatan F. ^{[2
]}

Oliveira, Jobson Q. ^{[3
]}

机构：

[1] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil

[2] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil

[3] Univ Estadual Ceara, Fac Educ Ciencias & Letras Sertao Cent, BR-63900000 Quixada, Ceara, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 197卷

关键词：

Riemannian warped product; H-2-hypersurfaces; Local rigidity; Bifurcation instants; Morse index; STABILITY; TORI;

D O I：

10.1016/j.na.2020.111865

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a Riemannian warped product I x (f) M-n, where I subset of R is an open interval, f is a positive real function defined on I and M-n is a compact Riemannian manifold without boundary, we use equivariant bifurcation theory in order to establish sufficient conditions, in terms of f and the spectrum of the Laplacian on M-n, that allow us to guarantee the existence of bifurcation instants or the local rigidity of a certain family of open sets whose boundaries are H-2-hypersurfaces, namely, whose boundaries are hypersurfaces with constant second mean curvature H-2. For each of our results, we have provided a considerable number of examples that verify all the assumptions under consideration. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：20

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