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On the Genus and Area of Constant Mean Curvature Surfaces with Bounded Index
The Journal of Geometric Analysis ( IF 1.1 ) Pub Date : 2021-06-10 , DOI: 10.1007/s12220-021-00708-y
Artur B. Saturnino

Using the local picture of the degeneration of sequences of minimal surfaces developed by Chodosh et al. (Invent Math 209(3):617–664, [1]) we show that in any closed Riemannian 3-manifold (Mg), the genus of an embedded CMC surface can be bounded only in terms of its index and area, independently of the value of its mean curvature. We also show that if M has finite fundamental group, the genus and area of any non-minimal embedded CMC surface can be bounded in term of its index and a lower bound for its mean curvature.



中文翻译:

关于具有有界指数的等平均曲率曲面的属和面积

使用由 Chodosh 等人开发的最小表面序列退化的局部图像。(Invent Math 209(3):617–664, [1]) 我们表明,在任何封闭的黎曼 3-流形 ( Mg ) 中,嵌入的 CMC 曲面的属只能在其索引和面积方面有界,与其平均曲率值无关。我们还表明,如果M具有有限的基本群,则任何非最小嵌入 CMC 表面的属和面积都可以根据其指数和平均曲率的下限而有界。

更新日期:2021-06-11
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