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

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

Download 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

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

Subjects:
Primary: 53A10
Secondary: 49Q05, 53C42

Rights: Copyright © 2019 Institut Mittag-Leffler

JOURNAL ARTICLE
37 PAGES


SHARE
Vol.223 • No. 1 • September 2019
Back to Top