We prove index estimates for closed and free boundary CMC surfaces in certain 3-dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are able to prove that the index of a CMC surface in an arbitrary 3-manifold is bounded below by a linear function of its genus.

中文翻译：

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3维流形中具有恒定平均曲率的曲面的索引估计

我们证明了某些欧几里得空间的某些3维子流形中封闭和自由边界CMC表面的指数估计。当平均曲率足够大时，我们可以证明CMC曲面在任意3个歧管中的索引受其属的线性函数限制在下方。