论文标题
双曲线空间中恒定高阶平均曲率的超曲面的独特性
Uniqueness of Hypersurfaces of Constant Higher Order Mean Curvature in Hyperbolic Space
论文作者
论文摘要
我们研究了在不同条件下双曲空空间中h旋磷和等距球的独特性。首先，我们将Do Carmo和Lawson概括为具有恒定高阶平均曲率的嵌入式超曲面。然后，我们证明了在不同假设下的浸入式超浮标的两种伯恩斯坦类型结果。最后，我们从halospheres和等距球的较高平均曲率方面显示了刚性的刚性。
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.
