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arXiv · 1605.02501

Bounds on the topology and index of minimal surfaces

William H. Meeks III·Joaquin Perez·Antonio Ros
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Abstract

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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William H. Meeks III, Joaquin Perez, Antonio Ros. 2016-05-09. Bounds on the topology and index of minimal surfaces. https://arxiv.org/abs/1605.02501

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