We prove that for every non-negative 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.

William H. Meeks

Joaquín Pérez

Antonio Ros

Acta Mathematica

发表所有数学领域最高质量的原创研究论文。

The journal Acta Mathematica is dedicated to publishing original research papers of the highest quality across all areas of mathematics.

《Acta Mathematica》期刊致力于发表所有数学领域内最高质量的原创研究论文。

Category	Quartile
数学	1
数学, 数学	1

Bounds on the topology and index of minimal surfaces

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