Hypersurfaces of constant higher order mean curvature in warped products-Reference-Cited by-同舟云学术

Hypersurfaces of constant higher order mean curvature in warped products

Published:2012-09-12 Issue:2 Volume:365 Page:591-621
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Alías Luis,Impera Debora,Rigoli Marco

Abstract

In this paper we characterize compact and complete hypersurfaces with some constant higher order mean curvature into warped product spaces. Our approach is based on the use of a new trace operator version of the Omori-Yau maximum principle which seems to be interesting in its own.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2013-365-02/S0002-9947-2012-05774-6/S0002-9947-2012-05774-6.pdf

Reference15 articles.

1. A characteristic property of spheres;Alexandrov, A. D.;Ann. Mat. Pura Appl. (4),1962

2. Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes;Alías, Luis J.;Math. Proc. Cambridge Philos. Soc.,2007

3. Uniqueness of constant mean curvature surfaces properly immersed in a slab;Alías, Luis J.;Comment. Math. Helv.,2006

4. Constant mean curvature hypersurfaces in warped product spaces;Alías, Luis J.;Proc. Edinb. Math. Soc. (2),2007

5. Constant higher-order mean curvature hypersurfaces in Riemannian spaces;Alías, Luis J.;J. Inst. Math. Jussieu,2006

Cited by 41 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the stability of constant higher order mean curvature hypersurfaces in a Riemannian manifold;Mathematische Nachrichten;2024-09

2. Rigidity and nonexistence of complete hypersurfaces via Liouville type results and other maximum principles, with applications to entire graphs;Asymptotic Analysis;2023-11-10

3. Hopf type theorems for surfaces in the de Sitter–Schwarzschild and Reissner–Nordstrom manifolds;Annali di Matematica Pura ed Applicata (1923 -);2023-10-27

4. Poincaré type inequality for hypersurfaces and rigidity results;Journal of Differential Equations;2023-10

5. Curvature estimates for graphs in warped product spaces;Differential Geometry and its Applications;2023-02