Finite time singularities for Lagrangian mean curvature flow. (English) Zbl 1315.53074

The main result of the paper is as follows: let \(M\) be a Calabi-Yau manifold of real dimension 4 and \(\Sigma\) an embedded Lagrangian in \(M\). Then there exists a Lagrangian \(L\) which is Hamiltonian isotopic to \(\Sigma\) and so that the Lagrangian mean curvature flow with initial condition \(L\) has a finite time singularity. This disproves a conjecture of Mu-Tao Wang which is a weaker version of a conjecture of Thomas-Yau concerning long time existence (and convergence) of Lagrangian mean curvature flow satisfying a condition of stability.


53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53D12 Lagrangian submanifolds; Maslov index
Full Text: DOI arXiv


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