Special Lagrangians, stable bundles and mean curvature flow

R. P. Thomas; S. -T. Yau

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arXiv · math/0104197

Special Lagrangians, stable bundles and mean curvature flow

R. P. Thomas·S. -T. Yau

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Abstract

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-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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BibTeX RIS

R. P. Thomas, S. -T. Yau. 2002-12-16. Special Lagrangians, stable bundles and mean curvature flow. https://arxiv.org/abs/math/0104197

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