References
Chau, A., Chen J.Y., He, W.Y.: Lagrangian mean curvature flow for entire Lipschitz graphs. ar**v:0902.3300v1
Chen J, He W.Y.: A note on sigular time of mean curvature flow. Math. Z 266(4), 921–931 (2010)
Chen X.X, Li H.: Stability of Kähler-Ricci flow. J. Geom. Anal 20(2), 306–334 (2010)
Chen X.X., Li H., Wang B.: On the Kähler-Ricci flow with small initial energy. Geom. Funct. Anal. 18-5, 1525–1563 (2008)
Chen J., Li J.: Mean curvature flow of surfaces in 4-manifolds. Adv. Math. 163, 287–309 (2001)
Chen J., Li J.: Singularity of mean curvature flow of Lagrangian submanifolds. Invent. Math. 156(1), 25–51 (2004)
Chen B.L., Yin L.: Uniqueness and pseudolocality theorems of the mean curvature flow. Commun. Anal. Geom. 15(3), 435–490 (2007)
Han X., Li J.: The mean curvature flow approach to the symplectic isotopy problem. Int. Math. Res. Not. 26, 1611–1620 (2005)
Han X, Li J.: Singularities of symplectic and Lagrangian mean curvature flows. Front. Math. China 4(2), 283–296 (2009)
Hoffman, D., Spruck, J.: Sobolev and isoperimetric inequalities for Riemannian submanifolds. Commun. Pure. Appl. Math. 27, 715–727 (1974). Corrigendum: Commun. Pure. Appl. Math. 28, 765–766 (1975)
Lee Y.I.: Lagrangian minimal surfaces in Kähler-Einstein surfaces of negative scalar curvature. Commun. Anal. Geom. 2, 579–592 (1994)
Neves A.: Singularities of Lagrangian mean curvature flow: zero-Maslov class case. Invent. Math. 168(3), 449–484 (2007)
Neves A.: Singularities of Lagrangian mean curvature flow: monotone case. Math. Res. Lett 17, 109–126 (2010)
Oh Y.: Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds. Invent. Math. 101(2), 501–519 (1990)
Oh Y.: Volume minimization of Lagrangian submanifolds under Hamiltonian defromations. Math. Z. 212, 175–192 (1993)
Ono H.: Minimal Lagrangian submanifolds in adjoint orbits and upper bounds on the first eigenvalue of the Laplacian. J. Math. Soc. Jpn. 55(1), 243–254 (2003)
Perelman, G.: The entropy formula for the Ricci flow and its geometric applications. ar**v:math/0211159
Smoczyk, K.: A canonical way to deform a Lagrangian submanifold. ar**v:dg-ga/9605005v2
Smoczyk K.: Angle theorems for the Lagrangian mean curvature flow. Math. Z. 240, 849–883 (2002)
Smoczyk K.: Long time existence of the Lagrangian mean curvature flow. Calc. Var. 20, 25–46 (2004)
Smoczyk K.: Harnack inequality for the Lagrangian mean curvature flow. Calc. Var. 8, 247–258 (1999)
Smoczyk K., Wang M.T.: Mean curvature flows for Lagrangian submanifolds with convex potentials. J. Differ. Geom. 62, 243–257 (2002)
Strominger A., Yau S.-T., Zaslow E.: Mirror symmetry is T-duality. Nucl. Phys. B 479(1C2), 243–259 (1996)
Thomas R.P., Yau S.-T.: Special Lagrangians, stable bundles and mean curvature flow. Commun. Anal. Geom. 10, 1075–1113 (2002)
Wang M.T.: Mean curvature flow of surfaces in Einstein four-manifolds. J. Differ. Geom. 57(2), 301–338 (2001)
Wang, M.T.: A convergence result of the Lagrangian mean curvature flow. In: Proceedings of the Third International Congress of Chinese Mathematicians. AMS/IP Studies in Advanced Mathematics, vol. 42, Part 1 and 2, pp. 291–295. American Mathematical Society, Providence, RI (2008)
Wang, M.T.: Some recent developments in Lagrangian mean curvature flows. In: Surveys in Differential Geometry. Geometric flows, vol. XII, pp. 333–347. International Press, Somerville, MA (2008)
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H. Li’s research was supported in part by National Science Foundation of China No. 11001080 and a startup funding from University of Science and Technology of China.
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Li, H. Convergence of Lagrangian mean curvature flow in Kähler–Einstein manifolds. Math. Z. 271, 313–342 (2012). https://doi.org/10.1007/s00209-011-0865-z
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DOI: https://doi.org/10.1007/s00209-011-0865-z