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arXiv · 2010.01322

Barrier methods for minimal submanifolds in the Gibbons-Hawking ansatz

Federico Trinca
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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.

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Federico Trinca. 2020-10-03. Barrier methods for minimal submanifolds in the Gibbons-Hawking ansatz. https://arxiv.org/abs/2010.01322

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