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


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.


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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.


Received: 9 May 2016; Published: September 2019
First available in Project Euclid: 16 April 2020

zbMATH: 1428.53018
MathSciNet: MR4018264
Digital Object Identifier: 10.4310/ACTA.2019.v223.n1.a2

Primary: 53A10
Secondary: 49Q05 , 53C42

Keywords: curvature estimates , finite total curvature , index of stability , minimal lamination , minimal surface , removable singularity

Rights: Copyright © 2019 Institut Mittag-Leffler


Vol.223 • No. 1 • September 2019
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