Bounds on the topology and index of minimal surfaces

William H. Meeks, III University of Massachusetts Joaquín Pérez University of Granada Antonio Ros University of Granada

Differential Geometry mathscidoc:1911.43043

Acta Mathematica, 223, (1), 113 – 149, 2019
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 R3 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.
minimal surface, index of stability, curvature estimates, finite total curvature, minimal lamination, removable singularity
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@inproceedings{william2019bounds,
  title={Bounds on the topology and index of minimal surfaces},
  author={William H. Meeks, III, Joaquín Pérez, and Antonio Ros},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128155048540911554},
  booktitle={Acta Mathematica},
  volume={223},
  number={1},
  pages={113 – 149},
  year={2019},
}
William H. Meeks, III, Joaquín Pérez, and Antonio Ros. Bounds on the topology and index of minimal surfaces. 2019. Vol. 223. In Acta Mathematica. pp.113 – 149. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128155048540911554.
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