Singularities of Lagrange mean curvature flow: monotone case
type: Item
instance of: scholarly article
title: Singularities of Lagrange mean curvature flow: monotone case
zbMATH Open document ID: 1237.53068
author: André Neves
published in: Mathematical Research Letters
publication date: 2011-08-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0608401
review text: The author studies the formation of singularities for the mean curvature flow of a monotone Lagrangian in \(\mathbb{C}^n\) with initial condition a Lagrangian in \(\mathbb{C}^n\) for which the Liouville class equals the Maslov class. He proves that if the singularity occurs before the critical time, then the tangent flow at the singularity can be decomposed into a finite union of area-minimizing Lagrangian cones (slag cones). When \(n=2\), he proves that each connected component of the rescaled flow converges to an area-minimizing cone (slag cone). Explicit examples in which such singularity formation occurs are also given.
reviewed by: Shu-Yu Hsu
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 53C38
Mathematics Subject Classification ID: 53D12
zbMATH DE Number: 5937358
zbMATH Keywords: singularities
zbMATH Keywords: Lagrange mean curvature flow
zbMATH Keywords: slag cones
MaRDI profile type: Publication
arXiv ID: math/0608401
DOI: 10.4310/MRL.2010.V17.N1.A9
description: scientific article