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New characterizations of spacelike hyperplanes in the steady state space

New characterizations of spacelike hyperplanes in the steady state space <jats:p>In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb {S}^{n+1}_{1}$ which is known as the steady state space $\mathcal {H}^{n+1}$. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of $\mathcal {H}^{n+1}$. Furthermore, through the analysis of the hyperbolic cylinders of $\mathcal {H}^{n+1}$, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.</jats:p> http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png MATHEMATICA SCANDINAVICA CrossRef

New characterizations of spacelike hyperplanes in the steady state space

MATHEMATICA SCANDINAVICA , Volume 126 (1): 61-72 – Mar 29, 2020

New characterizations of spacelike hyperplanes in the steady state space


Abstract

<jats:p>In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb {S}^{n+1}_{1}$ which is known as the steady state space $\mathcal {H}^{n+1}$. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of $\mathcal {H}^{n+1}$. Furthermore, through the analysis of the hyperbolic cylinders of $\mathcal {H}^{n+1}$, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.</jats:p>

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Publisher
CrossRef
ISSN
1903-1807
DOI
10.7146/math.scand.a-117703
Publisher site
See Article on Publisher Site

Abstract

<jats:p>In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb {S}^{n+1}_{1}$ which is known as the steady state space $\mathcal {H}^{n+1}$. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of $\mathcal {H}^{n+1}$. Furthermore, through the analysis of the hyperbolic cylinders of $\mathcal {H}^{n+1}$, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.</jats:p>

Journal

MATHEMATICA SCANDINAVICACrossRef

Published: Mar 29, 2020

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