Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz

Jason D. Lotay; Goncalo Oliveira

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arXiv · 2002.10391

Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz

Jason D. Lotay·Goncalo Oliveira

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Abstract

The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkaehler 4-manifolds, and thus Calabi-Yau 2-folds. In this setting, we prove versions of the Thomas conjecture on existence of special Lagrangian representatives of Hamiltonian isotopy classes of Lagrangians, and the Thomas-Yau conjecture on long-time existence of the Lagrangian mean curvature flow. We also make observations concerning closed geodesics, curve shortening flow and minimal surfaces.

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Jason D. Lotay, Goncalo Oliveira. 2020-02-24. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. https://arxiv.org/abs/2002.10391

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