论文标题
在带有界指数的恒定平均曲率表面的属和面积上
On the genus and area of constant mean curvature surfaces with bounded index
论文作者
论文摘要
使用Chodosh，Ketover和Maximo开发的最小表面序列序列退化的局部图片，我们表明，在任何封闭的Riemannian 3-manifold $（M，G）$中，嵌入式CMC表面的属只能按其平均曲率的价值限制。我们还表明，如果$ m $具有有限的基本组，那么任何非最小嵌入式CMC表面的属和面积都可以按其指数限制，并且对于其平均曲率的下限。
Using the local picture of the degeneration of sequences of minimal surfaces developed by Chodosh, Ketover and Maximo we show that in any closed Riemannian 3-manifold $(M,g)$, 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.
