Abstract
Height estimates are given for hypersurfaces immersed in a class of warped products of the type \(\mathbb {R}\times _{\rho } M^n\), under the assumption that some higher order mean curvatures are linearly related. When the fiber \(M^n\) is compact and such a hypersurface \(\Sigma ^n\) is noncompact, two-sided and properly immersed, we apply our height estimates in order to get information concerning the topology at infinity of \(\Sigma ^n\). Furthermore, when \(M^n\) is not necessarily compact, using a generalized version of the Omori–Yau maximum principle we establish new half-space theorems for these hypersurfaces.
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The second author is partially supported by CNPq, Brazil, Grant 303977/2015-9.
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de Lima, E.L., de Lima, H.F. Height estimates and topology at infinity of hypersurfaces immersed in a certain class of warped products. Aequat. Math. 92, 737–761 (2018). https://doi.org/10.1007/s00010-018-0552-9
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DOI: https://doi.org/10.1007/s00010-018-0552-9
Keywords
- Warped products
- Generalized linear Weingarten hypersurfaces
- Height estimates
- Two-sided hypersurfaces
- Half-space theorems