We study the uniqueness of horospheres and equidistant spheres in the hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson [12] to embedded hypersurfaces with constant higher order mean curvature. Then we prove two Bernstein type results for immersed hypersurfaces un- der different assumptions. Last, we show the rigidity of horospheres and equidistant spheres in terms of their higher order mean curvatures.
Uniqueness of hypersurfaces of constant higher order mean curvature in the hyperbolic space
Nelli Barbara;
2024-01-01
Abstract
We study the uniqueness of horospheres and equidistant spheres in the hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson [12] to embedded hypersurfaces with constant higher order mean curvature. Then we prove two Bernstein type results for immersed hypersurfaces un- der different assumptions. Last, we show the rigidity of horospheres and equidistant spheres in terms of their higher order mean curvatures.File in questo prodotto:
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