Abstract:

A submanifold of a Riemannian manifold is minimal if it is a critical point of the volume functional. Using the maximum principle, we have a way to construct barriers for compact minimal submanifolds.

The Gibbons–Hawking ansatz provides a large family of hyperkähler 4-manifolds with a compatible circle-action that includes the Euclidean space, the Eguchi–Hanson space, the Taub–NUT space and their multi-point generalization. We apply barrier arguments for compact minimal submanifolds in this setting. This approach gives results towards a classification of compact minimal submanifolds.

Slides of the talk