Mean curvature flow of monotone Lagrangian submanifolds
type: Item
instance of: scholarly article
title: Mean curvature flow of monotone Lagrangian submanifolds
zbMATH Open document ID: 1144.53084
author: Konrad Groh
author: Knut Smoczyk
author: Kai Zehmisch
author: Matthias Schwarz
published in: Mathematische Zeitschrift
publication date: 2007-08-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0606428
review text: The authors study the formation of singularities that monotone Lagrangian submanifolds in \({\mathbb C}^n\) develop under the mean curvature flow. In particular, they provide an estimate for the singular time in terms of the monotonicity constant of an embedded compact, oriented, monotone Lagrangian submanifold under the assumption that it remains embedded; and they provide results characterizing equality in this estimate. In the second part of the paper, the authors discuss equivariant Lagrangian submanifolds as a special case. They show that a certain class of embedded equivariant Lagrangian submanifolds is stable under the mean curvature flow and that both, type-1 as well as type-2 singularities occur within this class.
reviewed by: Udo Hertrich-Jeromin
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53D12
zbMATH DE Number: 5180789
zbMATH Keywords: Lagrangian submanifold
zbMATH Keywords: mean curvature flow
zbMATH Keywords: Maslov index
zbMATH Keywords: Liouville class
zbMATH Keywords: singularity
zbMATH Keywords: blow-up
MaRDI profile type: Publication
OpenAlex ID: W2036789219
arXiv ID: math/0606428
cites work: Construction of Lagrangian self-similar solutions to the mean curvature flow in \(\mathbb C^n\)
cites work: Lagrangian tori in a symplectic vector space and global symplectomorphisms
cites work: A note on mean curvature, Maslov class and symplectic area of Lagrangian immersions
cites work: Q4850930
cites work: Local Lagrangian 2-knots are trivial
cites work: Q4382057
cites work: Pseudo holomorphic curves in symplectic manifolds
cites work: Asymptotic behavior for singularities of the mean curvature flow
cites work: Q3918700
cites work: Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I
cites work: Q3367827
cites work: Angle theorems for the Lagrangian mean curvature flow
cites work: Symmetric hypersurfaces in Riemannian manifolds contracting to Lie groups by their mean curvature
cites work: Mean curvature flows of Lagrangians submanifolds with convex potentials.
DOI: 10.1007/S00209-007-0126-3
description: scientific article