Special Lagrangians, stable bundles and mean curvature flow

Details Special Lagrangians, stable bundles and mean curvature flow Special Lagrangians, stable bundles and mean curvature flow

2001-04-19

arxiv.org/abs/math/0104197v3

Communications in Analysis and Geometry 10, 1075-1113, 2002

Mathematics

Differential Geometry

36 pages, 4 figures. Minor referee's corrections

Scientific paper

We make a conjecture about mean curvature flow of Lagrangian submanifolds of Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the stability condition, and propose a Jordan-H\"older-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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