Special Lagrangians, stable bundles and mean curvature flow

2001/04/30 by R. P. Thomas, S. -T. Yau · 3 citations
Mathematics · Physics and Astronomy · #math.DG #hep-th #math.AG #math.SG #msc:14J32 #msc:53C44

paper · pdf

published as Communications in Analysis and Geometry 10, 1075-1113, 2002 · 36 pages, 4 figures. Minor referee's corrections

arxiv created 2002/12/16 · arxiv updated 2009/11/30

Abstract

We make a conjecture about mean curvature flow of Lagrangian submanifolds of Calabi-Yau manifolds, expanding on \citeTh. We give new results about the stability condition, and propose a Jordan-Hölder-type decomposition of (special) Lagrangians. The main results are the uniqueness of special Lagrangians in hamiltonian deformation classes of Lagrangians, under mild conditions, and a proof of the conjecture in some cases with symmetry: mean curvature flow converging to Shapere-Vafa's examples of SLags.

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• Special Lagrangian sections and stability conditions on threefolds
• Rigidity and Classification of Legendrian Self-Shrinkers
• The Rigidity Theorem of Legendrian self-shrinkers

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