{"abstract":[{"text":"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.","lang":"eng"}],"publication_identifier":{"issn":["0022-040X"]},"language":[{"iso":"eng"}],"corr_author":"1","publication_status":"published","citation":{"short":"J.D. Lotay, G. Oliveira, Journal of Differential Geometry 126 (2024) 1121–1184.","ieee":"J. D. Lotay and G. Oliveira, “Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz,” <i>Journal of Differential Geometry</i>, vol. 126, no. 3. International Press, pp. 1121–1184, 2024.","ama":"Lotay JD, Oliveira G. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. <i>Journal of Differential Geometry</i>. 2024;126(3):1121-1184. doi:<a href=\"https://doi.org/10.4310/jdg/1717348872\">10.4310/jdg/1717348872</a>","apa":"Lotay, J. D., &#38; Oliveira, G. (2024). Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. <i>Journal of Differential Geometry</i>. International Press. <a href=\"https://doi.org/10.4310/jdg/1717348872\">https://doi.org/10.4310/jdg/1717348872</a>","chicago":"Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian Mean Curvature Flow and the Gibbons-Hawking Ansatz.” <i>Journal of Differential Geometry</i>. International Press, 2024. <a href=\"https://doi.org/10.4310/jdg/1717348872\">https://doi.org/10.4310/jdg/1717348872</a>.","ista":"Lotay JD, Oliveira G. 2024. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry. 126(3), 1121–1184.","mla":"Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian Mean Curvature Flow and the Gibbons-Hawking Ansatz.” <i>Journal of Differential Geometry</i>, vol. 126, no. 3, International Press, 2024, pp. 1121–84, doi:<a href=\"https://doi.org/10.4310/jdg/1717348872\">10.4310/jdg/1717348872</a>."},"year":"2024","department":[{"_id":"TaHa"}],"article_processing_charge":"No","date_created":"2024-07-22T07:45:31Z","publisher":"International Press","_id":"17292","volume":126,"type":"journal_article","status":"public","oa_version":"None","month":"03","page":"1121-1184","scopus_import":"1","publication":"Journal of Differential Geometry","date_updated":"2024-07-23T06:18:34Z","article_type":"original","title":"Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz","author":[{"last_name":"Lotay","first_name":"Jason D.","full_name":"Lotay, Jason D."},{"last_name":"Oliveira","first_name":"Goncalo","id":"58abbde8-f455-11eb-a497-98c8fd71b905","full_name":"Oliveira, Goncalo"}],"day":"01","issue":"3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2024-03-01T00:00:00Z","quality_controlled":"1","intvolume":"       126","doi":"10.4310/jdg/1717348872"}