Finite time singularities for Lagrangian mean curvature flow

• 成果类型: Article
• 署名作者: Neves, Andre
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.177.3.5
• 发表日期: 2013
• 页码: 1029-1076
• 关键词: parabolic equations; SURFACES; CURVES; intersections

摘要

Given any embedded Lagrangian on a four-dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class that develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lagrangian mean curvature flow.