Bounds on the topology and index of minimal surfaces

William H. Meeks; Joaquin Perez; Antonio Ros

Bounds on the topology and index of minimal surfaces

Differential Geometry 2019-09-19 v2

Authors: William H. Meeks , Joaquin Perez , Antonio Ros

Abstract

We prove that for every nonnegative 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.

Keywords

minimal surface embedded surface finite topology number of ends stability index genus bound

Cite

@article{arxiv.1605.02501,
  title  = {Bounds on the topology and index of minimal surfaces},
  author = {William H. Meeks and Joaquin Perez and Antonio Ros},
  journal= {arXiv preprint arXiv:1605.02501},
  year   = {2019}
}

Comments

31 pages, 9 figures. Final version to appear in Acta Mathematica

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