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Lagrangian mean curvature flow of Whitney spheres

Andreas Savas-Halilaj and Knut Smoczyk

Geometry & Topology 23 (2019) 1057–1084

It is shown that an equivariant Lagrangian sphere with a positivity condition on its Ricci curvature develops a type-II singularity under the Lagrangian mean curvature flow that rescales to the product of a grim reaper with a flat Lagrangian subspace. In particular this result applies to the Whitney spheres.

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Lagrangian mean curvature flow, equivariant Lagrangian submanifolds, type-II singularities
Mathematical Subject Classification 2010
Primary: 53C21, 53C42, 53C44
Received: 4 April 2018
Accepted: 13 July 2018
Published: 8 April 2019
Proposed: Tobias H Colding
Seconded: Gang Tian, Bruce Kleiner
Andreas Savas-Halilaj
Department of Mathematics
University of Ioannina
Knut Smoczyk
Institute of Differential Geometry
Leibniz University Hannover