The stability of hypersurfaces with constant shifted k‐th mean curvature

In this paper, we prove the rigidity for the compact stable hypersurfaces with constant shifted k‐th curvature in hyperbolic spaces.

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References (14)

(1962)
Uniqueness theorems for surfaces in the large. V
G. Solanes (2005)
Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces
Transactions of the American Mathematical Society, 358
Linfen Cao, Haizhong Li (2007)
r-Minimal submanifolds in space forms
Annals of Global Analysis and Geometry, 32
João Barbosa, A. Colares (1997)
Stability of Hypersurfaces with Constant $$r$$ -Mean Curvature
Annals of Global Analysis and Geometry, 15
(1962)
Uniqueness theorems for surfaces in the large
J. Barbosa, M. Carmo, J. Eschenburg (1988)
Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
Mathematische Zeitschrift, 197
Alencar H. (1993)
117
Math. Z., 213
H. Alencar, W. Santos, Detang Zhou (1993)
Stable hypersurfaces with constant scalar curvature
Mathematische Zeitschrift, 213
Haizhong Li, Yong Wei, Changwei Xiong (2014)
A note on Weingarten hypersurfaces in the warped product manifold
International Journal of Mathematics, 25
H. Rosenberg (1993)
Hypersurfaces of constant curvature in space forms
Bulletin Des Sciences Mathematiques, 117
J. L. M. Barbosa, A. G. Colares (1997)
Stability of hypersurfaces with constant r‐mean curvature
, 15
J. Barbosa, M. Docarmo (1981)
Stability of hypersurfaces of constant mean curvature
Aleksandrov A. D. (1962)
412
Amer. Math. Soc. Transl. (2), 21
B. Andrews, Xuzhong Chen, Yong Wei (2018)
Volume preserving flow and Alexandrov–Fenchel type inequalities in hyperbolic space
Journal of the European Mathematical Society