In this paper, we obtain new parametric uniqueness results for complete constant weighted mean curvature hypersurfaces under suitable geometric assumptions in weighted warped products. Furthermore, we also prove very general Bernstein type results for the constant mean curvature equation for entire graphs in these ambient spaces.

中文翻译：

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新的伯恩斯坦类型导致加权翘曲产品

在本文中，我们在加权翘曲产品的适当几何假设下获得了完整的恒定加权平均曲率超曲面的新参数唯一性结果。此外，我们还证明了这些环境空间中整个图形的恒定平均曲率方程的非常通用的Bernstein型结果。