拓扑的边界和最小曲面的索引

IF 4.9 1区数学 Q1 MATHEMATICS

Acta Mathematica Pub Date : 2016-05-09 DOI:10.4310/acta.2019.v223.n1.a2

W. Meeks, Joaquín Pérez, A. Ros

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引用次数: 7

摘要

证明了对于每一个非负整数$g$，在$\mathbb{R}^3$属$g$和有限拓扑$ mathbb{R}^3$中存在一个完整的嵌入极小曲面$M$的端数的界。当$M$至少有两个端点时，$M$的有限端点数的这个界意味着$M$具有有限的稳定性指标，该指标由一个仅依赖于其属的常数限定。

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Bounds on the topology and index of minimal surfaces

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.

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