Abstract
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.
Citation
William H. Meeks III. Joaquín Pérez. Antonio Ros. "Bounds on the topology and index of minimal surfaces." Acta Math. 223 (1) 113 - 149, September 2019. https://doi.org/10.4310/ACTA.2019.v223.n1.a2
Information