English

Barrier methods for minimal submanifolds in the Gibbons-Hawking ansatz

Differential Geometry 2022-06-13 v2

Abstract

We describe a barrier argument for compact minimal submanifolds in the multi-Eguchi-Hanson and in the multi-Taub-NUT spaces, which are hyperkaehler 4-manifolds given by the Gibbons-Hawking ansatz. This approach is used to obtain results towards a classification of compact minimal submanifolds in this setting. We also prove a converse of Tsai and Wang's result that relates the strong stability condition to the convexity of the distance function.

Keywords

Cite

@article{arxiv.2010.01322,
  title  = {Barrier methods for minimal submanifolds in the Gibbons-Hawking ansatz},
  author = {Federico Trinca},
  journal= {arXiv preprint arXiv:2010.01322},
  year   = {2022}
}

Comments

34 pages, 9 figures