Uniqueness of Hypersurfaces of Constant Higher Order Mean Curvature in Hyperbolic Space
Barbara Nelli and Jingyong Zhu
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Submission date: 26. Aug. 2020
Link to arXiv:See the arXiv entry of this preprint.
We study the uniqueness of horospheres and equidistant spheres in hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson to the embedded hypersurfaces with constant higher order mean curvature. Then we prove two Bernstein type results for immersed hypersurfaces under different assumptions. Last, we show the rigidity of horospheres and equidistant spheres in terms of their higher order mean curvatures.