Index of the critical catenoid

Baptiste Devyver

Index of the critical catenoid

Differential Geometry 2018-04-12 v2

Authors: Baptiste Devyver

Abstract

In this article, we show that the critical catenoid, as a free boundary minimal surface of the unit ball in $\mathbb{R}^3$ , has index $4$ . We also prove that a free boundary minimal surface of the unit ball in $\mathbb{R}^3$ , that is not a flat disk, has index at least $4$ .

Keywords

critical catenoid free boundary minimal surface Morse index unit ball

Cite

@article{arxiv.1609.02315,
  title  = {Index of the critical catenoid},
  author = {Baptiste Devyver},
  journal= {arXiv preprint arXiv:1609.02315},
  year   = {2018}
}

Comments

Improved presentation and references updated concerning the nullity. See also related results by G. Smith and D. Zhou arXiv:1609.01485, and H. Tran arXiv:1609.01651

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