Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz
Lotay JD, Oliveira G. 2024. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry. 126(3), 1121–1184.
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Author
Lotay, Jason D.;
Oliveira, GoncaloISTA
Corresponding author has ISTA affiliation
Department
Abstract
The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkähler 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 longtime existence of the Lagrangian mean curvature ow. We also make observations concerning closed geodesics, curve shortening flow and minimal surfaces.
Publishing Year
Date Published
2024-03-01
Journal Title
Journal of Differential Geometry
Publisher
International Press of Boston
Volume
126
Issue
3
Page
1121-1184
ISSN
IST-REx-ID
Cite this
Lotay JD, Oliveira G. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry. 2024;126(3):1121-1184. doi:10.4310/jdg/1717348872
Lotay, J. D., & Oliveira, G. (2024). Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry. International Press of Boston. https://doi.org/10.4310/jdg/1717348872
Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian Mean Curvature Flow and the Gibbons-Hawking Ansatz.” Journal of Differential Geometry. International Press of Boston, 2024. https://doi.org/10.4310/jdg/1717348872.
J. D. Lotay and G. Oliveira, “Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz,” Journal of Differential Geometry, vol. 126, no. 3. International Press of Boston, pp. 1121–1184, 2024.
Lotay JD, Oliveira G. 2024. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry. 126(3), 1121–1184.
Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian Mean Curvature Flow and the Gibbons-Hawking Ansatz.” Journal of Differential Geometry, vol. 126, no. 3, International Press of Boston, 2024, pp. 1121–84, doi:10.4310/jdg/1717348872.
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