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
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. 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, 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, 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, 2024, pp. 1121–84, doi:10.4310/jdg/1717348872.
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