## Acta Mathematica

### Bounds on the topology and index of minimal surfaces

#### 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.

#### Article information

Source
Acta Math., Volume 223, Number 1 (2019), 113-149.

Dates
First available in Project Euclid: 16 April 2020

https://projecteuclid.org/euclid.acta/1587002478

Digital Object Identifier
doi:10.4310/ACTA.2019.v223.n1.a2

Mathematical Reviews number (MathSciNet)
MR4018264

Zentralblatt MATH identifier
1428.53018

#### Citation

Meeks, William H.; Pérez, Joaquín; Ros, Antonio. Bounds on the topology and index of minimal surfaces. Acta Math. 223 (2019), no. 1, 113--149. doi:10.4310/ACTA.2019.v223.n1.a2. https://projecteuclid.org/euclid.acta/1587002478