Lagrangian mean curvature flow of Whitney spheres

Savas-Halilaj, Andreas; Smoczyk, Knut

doi:10.2140/gt.2019.23.1057

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Lagrangian mean curvature flow of Whitney spheres

Andreas Savas-Halilaj and Knut Smoczyk

Geometry & Topology 23 (2019) 1057–1084

DOI: 10.2140/gt.2019.23.1057

Abstract

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.

Keywords

Lagrangian mean curvature flow, equivariant Lagrangian submanifolds, type-II singularities

Mathematical Subject Classification 2010

Primary: 53C21, 53C42, 53C44

References

Publication

Received: 4 April 2018

Accepted: 13 July 2018

Published: 8 April 2019

Proposed: Tobias H Colding

Seconded: Gang Tian, Bruce Kleiner

Authors

Andreas Savas-Halilaj
Department of Mathematics University of Ioannina Ioannina Greece

Knut Smoczyk
Institute of Differential Geometry Leibniz University Hannover Hannover Germany

Volume 23, issue 2 (2019)