Abstract
We prove the existence of rotational hypersurfaces in \({\mathbb{H}^n \times \mathbb{R}}\) with \({H_{r+1} = 0}\) (r-minimal hupersurfaces) and we classify them. Then we prove some uniqueness theorems for r-minimal hypersurfaces with a given (finite or asymptotic) boundary. In particular, we obtain a Schoen-type theorem for two ended complete hypersurfaces.
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Elbert, M.F., Nelli, B. & Santos, W. Hypersurfaces with \({H_{r+1}}\) = 0 in \({\mathbb{H}^n \times \mathbb{R}}\) . manuscripta math. 149, 507–521 (2016). https://doi.org/10.1007/s00229-015-0794-y
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DOI: https://doi.org/10.1007/s00229-015-0794-y