We prove that for every nonnegative integer $g$, there exists a bound on the number of ends of a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ of genus $g$ and finite topology. This bound on the finite number of ends when $M$ has at least two ends implies that $M$ has finite stability index which is bounded by a constant that only depends on its genus.

中文翻译：

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最小曲面的拓扑和索引的边界

我们证明，对于每个非负整数 $g$，在属 $g$ 和有限拓扑的 $\mathbb{R}^3$ 中的完整嵌入最小曲面 $M$ 的端点数存在一个界限。当 $M$ 至少有两个末端时，这个有限数量的末端的界限意味着 $M$ 具有有限的稳定性指数，该指数受一个常数限制，该常数仅取决于其属。